SherbyNet - /page/wikibook/entry.mu

<!DOCTYPE html>

<title>Frequency modulation</title>

</head>

<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Frequency modulation</span></span>

</h1>

</header>

/* start https://en.wikipedia.org/ */

.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}

/* end https://en.wikipedia.org/ */

</style><div role="note" class="hatnote navigation-not-searchable">For the application of frequency modulation to radio broadcasting, see <a href="FM_broadcasting" title="FM broadcasting">FM broadcasting</a>.</div>

<div role="note" class="hatnote navigation-not-searchable">"NFM" redirects here. For other uses, see <a href="NFM_(disambiguation)" class="mw-disambig" title="NFM (disambiguation)">NFM (disambiguation)</a>.</div>

/* start https://en.wikipedia.org/ */

.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}

/* end https://en.wikipedia.org/ */

</style><style data-mw-deduplicate="TemplateStyles:r1246091330">

/* start https://en.wikipedia.org/ */

.mw-parser-output .sidebar{width:22em;float:right;clear:right;margin:0.5em 0 1em 1em;background:var(--background-color-neutral-subtle,#f8f9fa);border:1px solid var(--border-color-base,#a2a9b1);padding:0.2em;text-align:center;line-height:1.4em;font-size:88%;border-collapse:collapse;display:table}body.skin-minerva .mw-parser-output .sidebar{display:table!important;float:right!important;margin:0.5em 0 1em 1em!important}.mw-parser-output .sidebar-subgroup{width:100%;margin:0;border-spacing:0}.mw-parser-output .sidebar-left{float:left;clear:left;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-none{float:none;clear:both;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-outer-title{padding:0 0.4em 0.2em;font-size:125%;line-height:1.2em;font-weight:bold}.mw-parser-output .sidebar-top-image{padding:0.4em}.mw-parser-output .sidebar-top-caption,.mw-parser-output .sidebar-pretitle-with-top-image,.mw-parser-output .sidebar-caption{padding:0.2em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-pretitle{padding:0.4em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-title,.mw-parser-output .sidebar-title-with-pretitle{padding:0.2em 0.8em;font-size:145%;line-height:1.2em}.mw-parser-output .sidebar-title-with-pretitle{padding:0.1em 0.4em}.mw-parser-output .sidebar-image{padding:0.2em 0.4em 0.4em}.mw-parser-output .sidebar-heading{padding:0.1em 0.4em}.mw-parser-output .sidebar-content{padding:0 0.5em 0.4em}.mw-parser-output .sidebar-content-with-subgroup{padding:0.1em 0.4em 0.2em}.mw-parser-output .sidebar-above,.mw-parser-output .sidebar-below{padding:0.3em 0.8em;font-weight:bold}.mw-parser-output .sidebar-collapse .sidebar-above,.mw-parser-output .sidebar-collapse .sidebar-below{border-top:1px solid #aaa;border-bottom:1px solid #aaa}.mw-parser-output .sidebar-navbar{text-align:right;font-size:115%;padding:0 0.4em 0.4em}.mw-parser-output .sidebar-list-title{padding:0 0.4em;text-align:left;font-weight:bold;line-height:1.6em;font-size:105%}.mw-parser-output .sidebar-list-title-c{padding:0 0.4em;text-align:center;margin:0 3.3em}@media(max-width:640px){body.mediawiki .mw-parser-output .sidebar{width:100%!important;clear:both;float:none!important;margin-left:0!important;margin-right:0!important}}body.skin--responsive .mw-parser-output .sidebar a>img{max-width:none!important}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}

/* end https://en.wikipedia.org/ */

</style><table class="sidebar nomobile nowraplinks skin-invert"><tbody><tr><th class="sidebar-title" style="background-color: #bdb"><a href="Passband" title="Passband">Passband</a> <a href="Signal_modulation" title="Signal modulation">modulation</a></th></tr><tr><td class="sidebar-image"><span typeof="mw:File"></span></td></tr><tr><th class="sidebar-heading" style="background-color: #cfc;">

<a href="Signal_modulation#Analog_modulation_methods" title="Signal modulation">Analog modulation</a></th></tr><tr><td class="sidebar-content hlist" style="color: black;">

<li><a href="Angle_modulation" title="Angle modulation">Angle modulation</a>

<ul>

</tr><tr><th class="sidebar-heading" style="background-color: #cfc;">

<a href="Signal_modulation#Digital_modulation_methods" title="Signal modulation">Digital modulation</a></th></tr><tr><td class="sidebar-content hlist" style="color: black;">

</tr><tr><th class="sidebar-heading" style="background-color: #cfc;">

<a href="Hierarchical_modulation" title="Hierarchical modulation">Hierarchical modulation</a></th></tr><tr><td class="sidebar-content hlist" style="color: black;">

</tr><tr><th class="sidebar-heading" style="background-color: #cfc;">

<a href="Spread_spectrum" title="Spread spectrum">Spread spectrum</a></th></tr><tr><td class="sidebar-content hlist" style="color: black;">

</tr><tr><th class="sidebar-heading" style="background-color: #cfc;">

See also</th></tr><tr><td class="sidebar-content hlist" style="color: black;">

<ul><li>Capacity-approaching codes</li>

<li><a href="Demodulation" title="Demodulation">Demodulation</a></li>

<li><a href="Line_code" title="Line code">Line coding</a></li>

<li><a href="Modem" title="Modem">Modem</a></li>

<li><a href="Multiplexing" title="Multiplexing">Multiplexing</a></li></ul></td>

</tr><tr><td class="sidebar-navbar"><style data-mw-deduplicate="TemplateStyles:r1239400231">

/* start https://en.wikipedia.org/ */

.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}

/* end https://en.wikipedia.org/ */

</style></td></tr></tbody></table>

<p><b>Frequency modulation</b> (<b>FM</b>) is a <a href="Signal_modulation" title="Signal modulation">signal modulation</a> technique used in electronic communication, originally for transmitting messages with a <a href="Radio_wave" title="Radio wave">radio wave</a>. In frequency modulation a <a href="Carrier_wave" title="Carrier wave">carrier wave</a> is varied in its <a href="Instantaneous_frequency" class="mw-redirect" title="Instantaneous frequency">instantaneous frequency</a> in proportion to a property, primarily the instantaneous amplitude, of a message signal, such as an <a href="Audio_signal" title="Audio signal">audio signal</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> The technology is used in <a href="Telecommunications" title="Telecommunications">telecommunications</a>, <a href="Radio_broadcasting" title="Radio broadcasting">radio broadcasting</a>, <a href="Signal_processing" title="Signal processing">signal processing</a>, and <a href="Run-length_limited#FM:_.280.2C1.29_RLL" title="Run-length limited">computing</a>.

</p><p>In <a href="Analog_signal" title="Analog signal">analog</a> frequency modulation, such as radio broadcasting of voice and music, the instantaneous <a href="Frequency_deviation" title="Frequency deviation">frequency deviation</a>, i.e. the difference between the frequency of the carrier and its center frequency, has a functional relation to the modulating signal amplitude.

</p><p><a href="Digital_data" title="Digital data">Digital data</a> can be encoded and transmitted with a type of frequency modulation known as <a href="Frequency-shift_keying" title="Frequency-shift keying">frequency-shift keying</a> (FSK), in which the instantaneous frequency of the carrier is shifted among a set of frequencies. The frequencies may represent digits, such as <i>0</i> and <i>1</i>. FSK is widely used in computer <a href="Modem" title="Modem">modems</a> such as <a href="Fax_modem" title="Fax modem">fax modems</a>, telephone <a href="Caller_ID" title="Caller ID">caller ID</a> systems, garage door openers, and other low-frequency transmissions.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> <a href="Radioteletype" title="Radioteletype">Radioteletype</a> also uses FSK.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>

</p><p>Frequency modulation is widely used for <a href="FM_broadcasting" title="FM broadcasting">FM radio</a> <a href="Broadcasting" title="Broadcasting">broadcasting</a>. It is also used in <a href="Telemetry" title="Telemetry">telemetry</a>, <a href="Radar" title="Radar">radar</a>, seismic prospecting, and monitoring <a href="Newborn" class="mw-redirect" title="Newborn">newborns</a> for seizures via <a href="EEG" class="mw-redirect" title="EEG">EEG</a>,<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> <a href="Two-way_radio" title="Two-way radio">two-way radio</a> systems, <a href="Frequency_modulation_synthesis" title="Frequency modulation synthesis">sound synthesis</a>, magnetic tape-recording systems and some video-transmission systems. In radio transmission, an advantage of frequency modulation is that it has a larger <a href="Signal-to-noise_ratio" title="Signal-to-noise ratio">signal-to-noise ratio</a> and therefore rejects <a href="Radio_frequency_interference" class="mw-redirect" title="Radio frequency interference">radio frequency interference</a> better than an equal power <a href="AM_broadcasting" title="AM broadcasting">amplitude modulation (AM)</a> signal. For this reason, most music is broadcast over FM radio.

</p><p>Frequency modulation and <a href="Phase_modulation" title="Phase modulation">phase modulation</a> are the two complementary principal methods of <a href="Angle_modulation" title="Angle modulation">angle modulation</a>; phase modulation is often used as an intermediate step to achieve frequency modulation. These methods contrast with <a href="Amplitude_modulation" title="Amplitude modulation">amplitude modulation</a>, in which the <a href="Amplitude" title="Amplitude">amplitude</a> of the carrier wave varies, while the frequency and phase remain constant.

</p>

<div class="mw-heading mw-heading2"><h2 id="Theory">Theory</h2></div>

/* start https://en.wikipedia.org/ */

.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}

/* end https://en.wikipedia.org/ */

</style>

<p>If the information to be transmitted (i.e., the <a href="Baseband_signal" class="mw-redirect" title="Baseband signal">baseband signal</a>) is <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{m}(t)}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle x_{m}(t)}</annotation>

</semantics>

</math></span><img src="./61d164c43cedb08b92aec5867090542cdb2e0c5a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.654ex; height:2.843ex;" alt="{\displaystyle x_{m}(t)}" loading="lazy"></span> and the <a href="Sinusoidal" class="mw-redirect" title="Sinusoidal">sinusoidal</a> carrier is <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{c}(t)=A_{c}\cos(2\pi f_{c}t)\,}">

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle x_{c}(t)=A_{c}\cos(2\pi f_{c}t)\,}</annotation>

</semantics>

</math></span><img src="./65ee4d4c9c6ad1d5ce0aaa782cc27b7bbc602684.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.821ex; height:2.843ex;" alt="{\displaystyle x_{c}(t)=A_{c}\cos(2\pi f_{c}t)\,}" loading="lazy"></span>, where <i>f<sub>c</sub></i> is the carrier's base frequency, and <i>A<sub>c</sub></i> is the carrier's amplitude, the modulator combines the carrier with the baseband data signal to get the transmitted signal:<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>

</p>

<mtr>

<mtd>

</mtd>

<mtd>

<msub>

</mrow>

</msub>

<mrow>

<mrow>

</mrow>

</mrow>

</msubsup>

</mrow>

</mrow>

</mtd>

</mtr>

<mtr>

<mtd>

<msub>

</mrow>

</msub>

<mrow>

<mrow>

</mrow>

</mrow>

</msubsup>

<mrow>

<mrow>

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

</mrow>

</mrow>

</mrow>

</mrow>

</mtd>

</mtr>

<mtr>

<mtd>

<msub>

</mrow>

</msub>

<mrow>

<mrow>

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

</mrow>

</mrow>

</msubsup>

<msub>

</mrow>

</msub>

</mrow>

</mrow>

</mtd>

</mtr>

</mtable>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}y(t)&=A_{c}\cos \left(2\pi \int _{0}^{t}f(\tau )d\tau \right)\\&=A_{c}\cos \left(2\pi \int _{0}^{t}\left[f_{c}+f_{\Delta }x_{m}(\tau )\right]d\tau \right)\\&=A_{c}\cos \left(2\pi f_{c}t+2\pi f_{\Delta }\int _{0}^{t}x_{m}(\tau )d\tau \right)\\\end{aligned}}}</annotation>

</semantics>

</math></span><img src="./5a85546c0eab3462755f52bf3808a8b9f5083b38.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -8.768ex; margin-bottom: -0.237ex; width:43.252ex; height:19.176ex;" alt="{\displaystyle {\begin{aligned}y(t)&=A_{c}\cos \left(2\pi \int _{0}^{t}f(\tau )d\tau \right)\\&=A_{c}\cos \left(2\pi \int _{0}^{t}\left[f_{c}+f_{\Delta }x_{m}(\tau )\right]d\tau \right)\\&=A_{c}\cos \left(2\pi f_{c}t+2\pi f_{\Delta }\int _{0}^{t}x_{m}(\tau )d\tau \right)\\\end{aligned}}}" loading="lazy"></span></dd></dl>

<p>where <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{\Delta }=K_{f}A_{m}}">

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle f_{\Delta }=K_{f}A_{m}}</annotation>

</semantics>

</math></span><img src="./220f0c0960e764c1f58b0e884d5a75146cdbfaf8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:12.366ex; height:2.843ex;" alt="{\displaystyle f_{\Delta }=K_{f}A_{m}}" loading="lazy"></span>, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K_{f}}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle K_{f}}</annotation>

</semantics>

</math></span><img src="./3900396f45aad0fe4532a59077aa070eba64b346.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.109ex; height:2.843ex;" alt="{\displaystyle K_{f}}" loading="lazy"></span> being the sensitivity of the frequency modulator and <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{m}}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A_{m}}</annotation>

</semantics>

</math></span><img src="./58f710c420b53609029176c7bf3717f9d79b0e50.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.418ex; height:2.509ex;" alt="{\displaystyle A_{m}}" loading="lazy"></span> being the amplitude of the modulating signal or baseband signal.

</p><p>In this equation, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(\tau )\,}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle f(\tau )\,}</annotation>

</semantics>

</math></span><img src="./e6f627bf71626ca98d36524f4e74fb969d44368e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.677ex; height:2.843ex;" alt="{\displaystyle f(\tau )\,}" loading="lazy"></span> is the <i><a href="Instantaneous_phase" class="mw-redirect" title="Instantaneous phase">instantaneous frequency</a></i> of the oscillator and <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{\Delta }\,}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle f_{\Delta }\,}</annotation>

</semantics>

</math></span><img src="./662e1ca76964e38802eb8ff0dd6baf055ef54550.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.127ex; height:2.509ex;" alt="{\displaystyle f_{\Delta }\,}" loading="lazy"></span> is the <i><a href="Frequency_deviation" title="Frequency deviation">frequency deviation</a></i>, which represents the maximum shift away from <i>f<sub>c</sub></i> in one direction, assuming <i>x</i><sub><i>m</i></sub>(<i>t</i>) is limited to the range ±1.

</p><p>This process of integrating the instantaneous frequency to create an instantaneous phase is different from adding the modulating signal to the carrier frequency

</p>

<mtr>

<mtd>

</mtd>

<mtd>

<msub>

</mrow>

</msub>

<mrow>

<mrow>

<mrow>

<mrow>

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

</mrow>

</mrow>

</mrow>

</mrow>

</mtd>

</mtr>

</mtable>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}y(t)&=A_{c}\cos \left(2\pi \left[f_{c}+f_{\Delta }x_{m}(t)\right]t\right)\end{aligned}}}</annotation>

</semantics>

</math></span><img src="./33e21e0bf408a5afae4268fde1d3ec3d0ca150c3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:34.369ex; height:2.843ex;" alt="{\displaystyle {\begin{aligned}y(t)&=A_{c}\cos \left(2\pi \left[f_{c}+f_{\Delta }x_{m}(t)\right]t\right)\end{aligned}}}" loading="lazy"></span></dd></dl>

<p>which would result in a modulated signal that has spurious local minima and maxima that do not correspond to those of the carrier.

</p><p>While most of the energy of the signal is contained within <i>f<sub>c</sub></i> ± <i>f</i><sub>Δ</sub>, it can be shown by <a href="Fourier_analysis" title="Fourier analysis">Fourier analysis</a> that a wider range of frequencies is required to precisely represent an FM signal. The <a href="Frequency_spectrum" class="mw-redirect" title="Frequency spectrum">frequency spectrum</a> of an actual FM signal has components extending infinitely, although their amplitude decreases and higher-order components are often neglected in practical design problems.<sup id="cite_ref-TGTSCS05_6-0" class="reference"><a href="#cite_note-TGTSCS05-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading3"><h3 id="Sinusoidal_baseband_signal">Sinusoidal baseband signal</h3></div>

<p>Mathematically, a baseband modulating signal may be approximated by a <a href="Sine_wave" title="Sine wave">sinusoidal</a> <a href="Continuous_wave" title="Continuous wave">continuous wave</a> signal with a frequency <i>f<sub>m</sub></i>. This method is also named as single-tone modulation. The integral of such a signal <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{m}(t)=cos(2\pi f_{m}t)}">

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle x_{m}(t)=cos(2\pi f_{m}t)}</annotation>

</semantics>

</math></span><img src="./30d4db02b7499422a7edf20be95727d112f2a212.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.935ex; height:2.843ex;" alt="{\displaystyle x_{m}(t)=cos(2\pi f_{m}t)}" loading="lazy"></span> is:

</p>

</mrow>

</mrow>

</msubsup>

<msub>

</mrow>

</msub>

<mfrac>

<mrow>

<mrow>

<mrow>

<msub>

</mrow>

</msub>

</mrow>

</mrow>

<mrow>

<msub>

</mrow>

</msub>

</mrow>

</mfrac>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \int _{0}^{t}x_{m}(\tau )d\tau ={\frac {\sin \left(2\pi f_{m}t\right)}{2\pi f_{m}}}\,}</annotation>

</semantics>

</math></span><img src="./9d563c457e757dd75aa1cc349770c517de3d9b67.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:27.246ex; height:6.176ex;" alt="{\displaystyle \int _{0}^{t}x_{m}(\tau )d\tau ={\frac {\sin \left(2\pi f_{m}t\right)}{2\pi f_{m}}}\,}" loading="lazy"></span></dd></dl>

<p>In this case, the expression for y(t) above simplifies to:

</p>

<msub>

</mrow>

</msub>

<mrow>

<mrow>

<msub>

</mrow>

</msub>

<mfrac>

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

<mrow>

<mrow>

<msub>

</mrow>

</msub>

</mrow>

</mrow>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle y(t)=A_{c}\cos \left(2\pi f_{c}t+{\frac {f_{\Delta }}{f_{m}}}\sin \left(2\pi f_{m}t\right)\right)\,}</annotation>

</semantics>

</math></span><img src="./5ee288fe8dc62138b29ab458f2c3d43c9586c90a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:40.005ex; height:6.176ex;" alt="{\displaystyle y(t)=A_{c}\cos \left(2\pi f_{c}t+{\frac {f_{\Delta }}{f_{m}}}\sin \left(2\pi f_{m}t\right)\right)\,}" loading="lazy"></span></dd></dl>

<p>where the amplitude <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{m}\,}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A_{m}\,}</annotation>

</semantics>

</math></span><img src="./ba62325b8ff8af350f350b2be029738f8f2537ac.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.805ex; height:2.509ex;" alt="{\displaystyle A_{m}\,}" loading="lazy"></span> of the modulating <a href="Sine_wave" title="Sine wave">sinusoid</a> is represented in the peak deviation <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{\Delta }=K_{f}A_{m}}">

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle f_{\Delta }=K_{f}A_{m}}</annotation>

</semantics>

</math></span><img src="./220f0c0960e764c1f58b0e884d5a75146cdbfaf8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:12.366ex; height:2.843ex;" alt="{\displaystyle f_{\Delta }=K_{f}A_{m}}" loading="lazy"></span> (see <a href="Frequency_deviation" title="Frequency deviation">frequency deviation</a>).

</p><p>The <a href="Harmonic" title="Harmonic">harmonic</a> distribution of a <a href="Sine_wave" title="Sine wave">sine wave</a> carrier modulated by such a <a href="Sinusoidal" class="mw-redirect" title="Sinusoidal">sinusoidal</a> signal can be represented with <a href="Bessel_function" title="Bessel function">Bessel functions</a>; this provides the basis for a mathematical understanding of frequency modulation in the frequency domain.

</p>

<div class="mw-heading mw-heading3"><h3 id="Modulation_index">Modulation index</h3></div>

<p>As in other modulation systems, the modulation index indicates by how much the modulated variable varies around its unmodulated level. It relates to variations in the <a href="Carrier_frequency" class="mw-redirect" title="Carrier frequency">carrier frequency</a>:

</p>

<mfrac>

<mrow>

</mrow>

</mrow>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

<mfrac>

<mrow>

<msub>

</mrow>

</msub>

<mrow>

<mrow>

<msub>

</mrow>

</msub>

</mrow>

</mrow>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle h={\frac {\Delta {}f}{f_{m}}}={\frac {f_{\Delta }\left|x_{m}(t)\right|}{f_{m}}}}</annotation>

</semantics>

</math></span><img src="./895e1b11648f886af1df8fbf1d3d100e72aabe36.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:22.497ex; height:6.176ex;" alt="{\displaystyle h={\frac {\Delta {}f}{f_{m}}}={\frac {f_{\Delta }\left|x_{m}(t)\right|}{f_{m}}}}" loading="lazy"></span></dd></dl>

<p>where <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{m}\,}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle f_{m}\,}</annotation>

</semantics>

</math></span><img src="./f4d42de6fb3509f332578213706975b7000eeb71.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.201ex; height:2.509ex;" alt="{\displaystyle f_{m}\,}" loading="lazy"></span> is the highest frequency component present in the modulating signal <i>x</i><sub><i>m</i></sub>(<i>t</i>), and <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta {}f\,}">

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \Delta {}f\,}</annotation>

</semantics>

</math></span><img src="./d71313180b08fae5bdaa5394b9ee5357815ecaa1.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.602ex; height:2.509ex;" alt="{\displaystyle \Delta {}f\,}" loading="lazy"></span> is the peak frequency-deviation – i.e. the maximum deviation of the <i><a href="Instantaneous_phase" class="mw-redirect" title="Instantaneous phase">instantaneous frequency</a></i> from the carrier frequency. For a sine wave modulation, the modulation index is seen to be the ratio of the peak frequency deviation of the carrier wave to the frequency of the modulating sine wave.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup>

</p><p>If <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h\ll 1}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle h\ll 1}</annotation>

</semantics>

</math></span><img src="./43dee7bea33845a4d3260d2e2452eb61458cd1a5.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.116ex; height:2.176ex;" alt="{\displaystyle h\ll 1}" loading="lazy"></span>, the modulation is called <b>narrowband FM</b> (NFM), and its bandwidth is approximately <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2f_{m}\,}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 2f_{m}\,}</annotation>

</semantics>

</math></span><img src="./6d1c8218ce172a3faacf5a0459fc0d66bfda1c67.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.364ex; height:2.509ex;" alt="{\displaystyle 2f_{m}\,}" loading="lazy"></span>. Sometimes modulation index <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h<0.3}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle h<0.3}</annotation>

</semantics>

</math></span><img src="./2a77b519f7d14db021bdb342f1caceef593b7be8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.409ex; height:2.176ex;" alt="{\displaystyle h<0.3}" loading="lazy"></span> is considered NFM and other modulation indices are considered wideband FM (WFM or FM).

</p><p>For digital modulation systems, for example, binary frequency shift keying (BFSK), where a binary signal modulates the carrier, the modulation index is given by:

</p>

<mfrac>

<mrow>

</mrow>

</mrow>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

<mfrac>

<mrow>

</mrow>

</mrow>

<mfrac>

<mrow>

<msub>

</mrow>

</msub>

</mrow>

</mfrac>

</mrow>

</mrow>

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle h={\frac {\Delta {}f}{f_{m}}}={\frac {\Delta {}f}{\frac {1}{2T_{s}}}}=2\Delta {}fT_{s}\ }</annotation>

</semantics>

</math></span><img src="./d50cea0bf54acffc4d1f9712ca3757d0e3061d90.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.671ex; width:26.248ex; height:7.343ex;" alt="{\displaystyle h={\frac {\Delta {}f}{f_{m}}}={\frac {\Delta {}f}{\frac {1}{2T_{s}}}}=2\Delta {}fT_{s}\ }" loading="lazy"></span></dd></dl>

<p>where <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{s}\,}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle T_{s}\,}</annotation>

</semantics>

</math></span><img src="./d256310d88e81d7bb03bd5702b567ff4355f041b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.748ex; height:2.509ex;" alt="{\displaystyle T_{s}\,}" loading="lazy"></span> is the symbol period, and <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{m}={\frac {1}{2T_{s}}}\,}">

<msub>

</mrow>

</msub>

<mfrac>

<mrow>

<msub>

</mrow>

</msub>

</mrow>

</mfrac>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle f_{m}={\frac {1}{2T_{s}}}\,}</annotation>

</semantics>

</math></span><img src="./4fc53184c7d17517830f510b9278315566b484ae.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:10.659ex; height:5.509ex;" alt="{\displaystyle f_{m}={\frac {1}{2T_{s}}}\,}" loading="lazy"></span> is used as the highest frequency of the modulating binary waveform by convention, even though it would be more accurate to say it is the highest <i>fundamental</i> of the modulating binary waveform. In the case of digital modulation, the carrier <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{c}\,}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle f_{c}\,}</annotation>

</semantics>

</math></span><img src="./3709bfd39334cb2fe8be041b8b4a8f7c568adce9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.471ex; height:2.509ex;" alt="{\displaystyle f_{c}\,}" loading="lazy"></span> is never transmitted. Rather, one of two frequencies is transmitted, either <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{c}+\Delta f}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle f_{c}+\Delta f}</annotation>

</semantics>

</math></span><img src="./236400b629e2ea9ae0fa7dfabd62655e1d59a074.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.138ex; height:2.509ex;" alt="{\displaystyle f_{c}+\Delta f}" loading="lazy"></span> or <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{c}-\Delta f}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle f_{c}-\Delta f}</annotation>

</semantics>

</math></span><img src="./fa305921b4471f018f8b948dda172a0358a326ee.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.138ex; height:2.509ex;" alt="{\displaystyle f_{c}-\Delta f}" loading="lazy"></span>, depending on the binary state 0 or 1 of the modulation signal.

</p><p>If <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h\gg 1}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle h\gg 1}</annotation>

</semantics>

</math></span><img src="./84bc7662efaae22ce831176ec7371a1e6a44ffe1.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.116ex; height:2.176ex;" alt="{\displaystyle h\gg 1}" loading="lazy"></span>, the modulation is called <i>wideband FM</i> and its bandwidth is approximately <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2f_{\Delta }\,}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 2f_{\Delta }\,}</annotation>

</semantics>

</math></span><img src="./5bad6782b6c6e31e67555364a8ec9fef684ed272.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.29ex; height:2.509ex;" alt="{\displaystyle 2f_{\Delta }\,}" loading="lazy"></span>. While wideband FM uses more bandwidth, it can improve the <a href="Signal-to-noise_ratio" title="Signal-to-noise ratio">signal-to-noise ratio</a> significantly; for example, doubling the value of <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta {}f\,}">

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \Delta {}f\,}</annotation>

</semantics>

</math></span><img src="./d71313180b08fae5bdaa5394b9ee5357815ecaa1.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.602ex; height:2.509ex;" alt="{\displaystyle \Delta {}f\,}" loading="lazy"></span>, while keeping <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{m}}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle f_{m}}</annotation>

</semantics>

</math></span><img src="./a86985ce29664569bf891b3c2e1350792aa04e7e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.814ex; height:2.509ex;" alt="{\displaystyle f_{m}}" loading="lazy"></span> constant, results in an eight-fold improvement in the signal-to-noise ratio.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> (Compare this with <a href="Chirp_spread_spectrum" title="Chirp spread spectrum">chirp spread spectrum</a>, which uses extremely wide frequency deviations to achieve processing gains comparable to traditional, better-known spread-spectrum modes).

</p><p>With a tone-modulated FM wave, if the modulation frequency is held constant and the modulation index is increased, the (non-negligible) bandwidth of the FM signal increases but the spacing between spectra remains the same; some spectral components decrease in strength as others increase. If the frequency deviation is held constant and the modulation frequency increased, the spacing between spectra increases.

</p><p>

Frequency modulation can be classified as narrowband if the change in the carrier frequency is about the same as the signal frequency, or as wideband if the change in the carrier frequency is much higher (modulation index > 1) than the signal frequency.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> For example, narrowband FM (NFM) is used for <a href="Two-way_radio" title="Two-way radio">two-way radio</a> systems such as <a href="Family_Radio_Service" title="Family Radio Service">Family Radio Service</a>, in which the carrier is allowed to deviate only 2.5 kHz above and below the center frequency with speech signals of no more than 3.5 kHz bandwidth. Wideband FM is used for <a href="FM_broadcasting" title="FM broadcasting">FM broadcasting</a>, in which music and speech are transmitted with up to 75 kHz deviation from the center frequency and carry audio with up to a 20 kHz bandwidth and subcarriers up to 92 kHz.

</p>

<div class="mw-heading mw-heading3"><h3 id="Bessel_functions">Bessel functions</h3></div>

<p>For the case of a carrier modulated by a single sine wave, the resulting frequency spectrum can be calculated using <a href="Bessel_function" title="Bessel function">Bessel functions</a> of the first kind, as a function of the <a href="Sideband" title="Sideband">sideband</a> number and the modulation index. The carrier and sideband amplitudes are illustrated for different modulation indices of FM signals. For particular values of the modulation index, the carrier amplitude becomes zero and all the signal power is in the sidebands.<sup id="cite_ref-TGTSCS05_6-1" class="reference"><a href="#cite_note-TGTSCS05-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>

</p><p>Since the sidebands are on both sides of the carrier, their count is doubled, and then multiplied by the modulating frequency to find the bandwidth. For example, 3 kHz deviation modulated by a 2.2 kHz audio tone produces a modulation index of 1.36. Suppose that we limit ourselves to only those sidebands that have a relative amplitude of at least 0.01. Then, examining the chart shows this modulation index will produce three sidebands. These three sidebands, when doubled, gives us (6 × 2.2 kHz) or a 13.2 kHz required bandwidth.

</p>

<th rowspan="2">Modulation<br>index

</th>

<th colspan="17">Sideband amplitude

</th></tr>

<tr>

<th>Carrier

</th>

<th>1

</th>

<th>2

</th>

<th>3

</th>

<th>4

</th>

<th>5

</th>

<th>6

</th>

<th>7

</th>

<th>8

</th>

<th>9

</th>

<th>10

</th>

<th>11

</th>

<th>12

</th>

<th>13

</th>

<th>14

</th>

<th>15

</th>

<th>16

</th></tr>

<tr>

<th>0.00

</th>

<td>1.00

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td></tr>

<tr>

<th>0.25

</th>

<td>0.98

</td>

<td>0.12

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td></tr>

<tr>

<th>0.5

</th>

<td>0.94

</td>

<td>0.24

</td>

<td>0.03

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td></tr>

<tr>

<th>1.0

</th>

<td>0.77

</td>

<td>0.44

</td>

<td>0.11

</td>

<td>0.02

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td></tr>

<tr>

<th>1.5

</th>

<td>0.51

</td>

<td>0.56

</td>

<td>0.23

</td>

<td>0.06

</td>

<td>0.01

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td></tr>

<tr>

<th>2.0

</th>

<td>0.22

</td>

<td>0.58

</td>

<td>0.35

</td>

<td>0.13

</td>

<td>0.03

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td></tr>

<tr>

<th>2.40483

</th>

<td>0.00

</td>

<td>0.52

</td>

<td>0.43

</td>

<td>0.20

</td>

<td>0.06

</td>

<td>0.02

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td></tr>

<tr>

<th>2.5

</th>

<td>−0.05

</td>

<td>0.50

</td>

<td>0.45

</td>

<td>0.22

</td>

<td>0.07

</td>

<td>0.02

</td>

<td>0.01

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td></tr>

<tr>

<th>3.0

</th>

<td>−0.26

</td>

<td>0.34

</td>

<td>0.49

</td>

<td>0.31

</td>

<td>0.13

</td>

<td>0.04

</td>

<td>0.01

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td></tr>

<tr>

<th>4.0

</th>

<td>−0.40

</td>

<td>−0.07

</td>

<td>0.36

</td>

<td>0.43

</td>

<td>0.28

</td>

<td>0.13

</td>

<td>0.05

</td>

<td>0.02

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td></tr>

<tr>

<th>5.0

</th>

<td>−0.18

</td>

<td>−0.33

</td>

<td>0.05

</td>

<td>0.36

</td>

<td>0.39

</td>

<td>0.26

</td>

<td>0.13

</td>

<td>0.05

</td>

<td>0.02

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td></tr>

<tr>

<th>5.52008

</th>

<td>0.00

</td>

<td>−0.34

</td>

<td>−0.13

</td>

<td>0.25

</td>

<td>0.40

</td>

<td>0.32

</td>

<td>0.19

</td>

<td>0.09

</td>

<td>0.03

</td>

<td>0.01

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td></tr>

<tr>

<th>6.0

</th>

<td>0.15

</td>

<td>−0.28

</td>

<td>−0.24

</td>

<td>0.11

</td>

<td>0.36

</td>

<td>0.36

</td>

<td>0.25

</td>

<td>0.13

</td>

<td>0.06

</td>

<td>0.02

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td></tr>

<tr>

<th>7.0

</th>

<td>0.30

</td>

<td>0.00

</td>

<td>−0.30

</td>

<td>−0.17

</td>

<td>0.16

</td>

<td>0.35

</td>

<td>0.34

</td>

<td>0.23

</td>

<td>0.13

</td>

<td>0.06

</td>

<td>0.02

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td></tr>

<tr>

<th>8.0

</th>

<td>0.17

</td>

<td>0.23

</td>

<td>−0.11

</td>

<td>−0.29

</td>

<td>−0.10

</td>

<td>0.19

</td>

<td>0.34

</td>

<td>0.32

</td>

<td>0.22

</td>

<td>0.13

</td>

<td>0.06

</td>

<td>0.03

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td></tr>

<tr>

<th>8.65373

</th>

<td>0.00

</td>

<td>0.27

</td>

<td>0.06

</td>

<td>−0.24

</td>

<td>−0.23

</td>

<td>0.03

</td>

<td>0.26

</td>

<td>0.34

</td>

<td>0.28

</td>

<td>0.18

</td>

<td>0.10

</td>

<td>0.05

</td>

<td>0.02

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td></tr>

<tr>

<th>9.0

</th>

<td>−0.09

</td>

<td>0.25

</td>

<td>0.14

</td>

<td>−0.18

</td>

<td>−0.27

</td>

<td>−0.06

</td>

<td>0.20

</td>

<td>0.33

</td>

<td>0.31

</td>

<td>0.21

</td>

<td>0.12

</td>

<td>0.06

</td>

<td>0.03

</td>

<td>0.01

</td>

<td>

</td>

<td>

</td>

<td>

</td></tr>

<tr>

<th>10.0

</th>

<td>−0.25

</td>

<td>0.04

</td>

<td>0.25

</td>

<td>0.06

</td>

<td>−0.22

</td>

<td>−0.23

</td>

<td>−0.01

</td>

<td>0.22

</td>

<td>0.32

</td>

<td>0.29

</td>

<td>0.21

</td>

<td>0.12

</td>

<td>0.06

</td>

<td>0.03

</td>

<td>0.01

</td>

<td>

</td>

<td>

</td></tr>

<tr>

<th>12.0

</th>

<td>0.05

</td>

<td>−0.22

</td>

<td>−0.08

</td>

<td>0.20

</td>

<td>0.18

</td>

<td>−0.07

</td>

<td>−0.24

</td>

<td>−0.17

</td>

<td>0.05

</td>

<td>0.23

</td>

<td>0.30

</td>

<td>0.27

</td>

<td>0.20

</td>

<td>0.12

</td>

<td>0.07

</td>

<td>0.03

</td>

<td>0.01

</td></tr></tbody></table>

<div class="mw-heading mw-heading3"><h3 id="Carson's_rule">Carson's rule</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Carson_bandwidth_rule" title="Carson bandwidth rule">Carson bandwidth rule</a></div>

<p>A <a href="Rule_of_thumb" title="Rule of thumb">rule of thumb</a>, <i>Carson's rule</i> states that nearly all (≈98 percent) of the power of a frequency-modulated signal lies within a <a href="Bandwidth_(signal_processing)" title="Bandwidth (signal processing)">bandwidth</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B_{T}\,}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B_{T}\,}</annotation>

</semantics>

</math></span><img src="./496ab4e30a92e0afdb2b4cfc605bf3c16d793d6d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.54ex; height:2.509ex;" alt="{\displaystyle B_{T}\,}" loading="lazy"></span> of:

</p>

<msub>

</mrow>

</msub>

<mrow>

<mrow>

<msub>

</mrow>

</msub>

</mrow>

</mrow>

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B_{T}=2\left(\Delta f+f_{m}\right)=2f_{m}(h+1)}</annotation>

</semantics>

</math></span><img src="./7abcb160893a755489aaf646dee1da1940926bf7.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:32.706ex; height:2.843ex;" alt="{\displaystyle B_{T}=2\left(\Delta f+f_{m}\right)=2f_{m}(h+1)}" loading="lazy"></span></dd></dl>

<p>where <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta f\,}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \Delta f\,}</annotation>

</semantics>

</math></span><img src="./2c92cbe9e6bd314168edaff405ec4fccdaaf94d9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.602ex; height:2.509ex;" alt="{\displaystyle \Delta f\,}" loading="lazy"></span>, as defined above, is the peak deviation of the instantaneous frequency <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(t)\,}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle f(t)\,}</annotation>

</semantics>

</math></span><img src="./a471e94c3479917173461b7045481220c91b6182.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.315ex; height:2.843ex;" alt="{\displaystyle f(t)\,}" loading="lazy"></span> from the center carrier frequency <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{c}}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle f_{c}}</annotation>

</semantics>

</math></span><img src="./d2b64a46c31800830b9fecc59b22812390e18c05.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.083ex; height:2.509ex;" alt="{\displaystyle f_{c}}" loading="lazy"></span>, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle h}</annotation>

</semantics>

</math></span><img src="./b26be3e694314bc90c3215047e4a2010c6ee184a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.339ex; height:2.176ex;" alt="{\displaystyle h}" loading="lazy"></span> is the modulation index which is the ratio of frequency deviation to highest frequency in the modulating signal, and <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{m}\,}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle f_{m}\,}</annotation>

</semantics>

</math></span><img src="./f4d42de6fb3509f332578213706975b7000eeb71.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.201ex; height:2.509ex;" alt="{\displaystyle f_{m}\,}" loading="lazy"></span>is the highest frequency in the modulating signal.

Carson's rule can only be applied to sinusoidal signals. For non-sinusoidal signals:

</p>

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B_{T}=2(\Delta f+W)=2W(D+1)}</annotation>

</semantics>

</math></span><img src="./afb109d82055ad98da28d56cb94186dd37fe9028.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:32.146ex; height:2.843ex;" alt="{\displaystyle B_{T}=2(\Delta f+W)=2W(D+1)}" loading="lazy"></span></dd></dl>

<p>where W is the highest frequency in the modulating signal but non-sinusoidal in nature and D is the Deviation ratio which is the ratio of frequency deviation to highest frequency of modulating non-sinusoidal signal.

</p>

<div class="mw-heading mw-heading2"><h2 id="Noise_reduction">Noise reduction</h2></div>

<p>FM provides improved <a href="Signal-to-noise_ratio" title="Signal-to-noise ratio">signal-to-noise ratio</a> (SNR), as compared for example with <a href="Amplitude_modulation" title="Amplitude modulation">AM</a>. Compared with an optimum AM scheme, FM typically has poorer SNR below a certain signal level called the noise threshold, but above a higher level – the full improvement or full quieting threshold – the SNR is much improved over AM. The improvement depends on modulation level and deviation. For typical voice communications channels, improvements are typically 5–15 dB. FM broadcasting using wider deviation can achieve even greater improvements. Additional techniques, such as pre-emphasis of higher audio frequencies with corresponding de-emphasis in the receiver, are generally used to improve overall SNR in FM circuits. Since FM signals have constant amplitude, FM receivers normally have limiters that remove AM noise, further improving SNR.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading2"><h2 id="Implementation">Implementation</h2></div>

<div class="mw-heading mw-heading3"><h3 id="Modulation">Modulation</h3></div>

<p>FM signals can be generated using either direct or indirect frequency modulation:

</p>

<ul><li>Direct FM modulation can be achieved by directly feeding the message into the input of a <a href="Voltage-controlled_oscillator" title="Voltage-controlled oscillator">voltage-controlled oscillator</a>.</li>

<li>For indirect FM modulation, the message signal is integrated to generate a <a href="Phase_modulation" title="Phase modulation">phase-modulated signal</a>. This is used to modulate a <a href="Crystal_oscillator" title="Crystal oscillator">crystal-controlled oscillator</a>, and the result is passed through a <a href="Frequency_multiplier" title="Frequency multiplier">frequency multiplier</a> to produce an FM signal. In this modulation, narrowband FM is generated leading to wideband FM later and hence the modulation is known as indirect FM modulation.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup></li></ul>

<div class="mw-heading mw-heading3"><h3 id="Demodulation">Demodulation</h3></div>

<div role="note" class="hatnote navigation-not-searchable">See also: <a href="Detector_(radio)#Frequency_and_phase_modulation_detectors" title="Detector (radio)">Detector (radio) § Frequency and phase modulation detectors</a></div>

<p>Many FM detector circuits exist. A common method for recovering the information signal is through a <a href="Foster%E2%80%93Seeley_discriminator" title="Foster–Seeley discriminator">Foster–Seeley discriminator</a> or <a href="Ratio_detector" title="Ratio detector">ratio detector</a>. A <a href="Phase-locked_loop" title="Phase-locked loop">phase-locked loop</a> can be used as an FM demodulator. <i>Slope detection</i> demodulates an FM signal by using a tuned circuit which has its resonant frequency slightly offset from the carrier. As the frequency rises and falls the tuned circuit provides a changing amplitude of response, converting FM to AM. AM receivers may detect some FM transmissions by this means, although it does not provide an efficient means of <a href="Detector_(radio)" title="Detector (radio)">detection</a> for FM broadcasts.

</p><p>In <a href="Software-defined_radio" title="Software-defined radio">software-defined radio</a> implementations, the demodulation may be carried out by using the <a href="Hilbert_transform" title="Hilbert transform">Hilbert transform</a> (implemented as a filter) to recover the instantaneous phase, and thereafter differentiating this phase (using another filter) to recover the instantaneous frequency. Alternatively, a complex mixer followed by a bandpass filter may be used to translate the signal to baseband, and then proceeding as before. For sampled signals, phase detection, and therefore frequency modulation detection, can be approximated by taking the IQ (complex) sample and multiplying it with the complex conjugate of the previous IQ sample, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x[n]\cdot {\overline {x[n-1]}}}">

<mover>

<mrow>

</mrow>

</mover>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle x[n]\cdot {\overline {x[n-1]}}}</annotation>

</semantics>

</math></span><img src="./8c02d0f694209d31ac9b9330e2b942318578fa50.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.833ex; height:3.676ex;" alt="{\displaystyle x[n]\cdot {\overline {x[n-1]}}}" loading="lazy"></span>.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> If the demodulated signal is sampled at or above Nyquist, this allows for recovery of near-instantaneous phase changes.

</p>

<div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2></div>

<div class="mw-heading mw-heading3"><h3 id="Doppler_effect">Doppler effect</h3></div>

<p>When an echolocating <a href="Bat" title="Bat">bat</a> approaches a target, its outgoing sounds return as echoes, which are Doppler-shifted upward in frequency. In certain species of bats, which produce constant frequency (CF) <a href="Animal_echolocation" title="Animal echolocation">echolocation</a> calls, the bats compensate for the <a href="Doppler_shift" class="mw-redirect" title="Doppler shift">Doppler shift</a> by lowering their call frequency as they approach a target. This keeps the returning echo in the same frequency range of the normal echolocation call. This dynamic frequency modulation is called the <b>Doppler Shift Compensation</b> (DSC), and was discovered by Hans Schnitzler in 1968.

</p>

<div class="mw-heading mw-heading3"><h3 id="Magnetic_tape_storage">Magnetic tape storage</h3></div>

<p>FM is also used at <a href="Intermediate_frequency" title="Intermediate frequency">intermediate frequencies</a> by analog <a href="Video_cassette_recorder" class="mw-redirect" title="Video cassette recorder">VCR</a> systems (including <a href="VHS" title="VHS">VHS</a>) to record the <a href="Luminance_(video)" class="mw-redirect" title="Luminance (video)">luminance</a> (black and white) portions of the video signal. Commonly, the <a href="Chrominance" title="Chrominance">chrominance</a> component is recorded as a conventional AM signal, using the higher-frequency FM signal as <a href="Tape_bias" title="Tape bias">bias</a>. FM is the only feasible method of recording the luminance ("black-and-white") component of video to (and retrieving video from) <a href="Magnetic_tape" title="Magnetic tape">magnetic tape</a> without distortion; video signals have a large range of frequency components – from a few <a href="Hertz" title="Hertz">hertz</a> to several <a href="Megahertz" class="mw-redirect" title="Megahertz">megahertz</a>, too wide for <a href="Equalization_(audio)" class="mw-redirect" title="Equalization (audio)">equalizers</a> to work with due to electronic noise below −60 <a href="Decibel" title="Decibel">dB</a>. FM also keeps the tape at saturation level, acting as a form of <a href="Noise_reduction" title="Noise reduction">noise reduction</a>; a <a href="Audio_level_compression" class="mw-redirect" title="Audio level compression">limiter</a> can mask variations in playback output, and the <a href="FM_capture" class="mw-redirect" title="FM capture">FM capture</a> effect removes <a href="Print-through" title="Print-through">print-through</a> and <a href="Pre-echo" title="Pre-echo">pre-echo</a>. A continuous pilot-tone, if added to the signal – as was done on <a href="V2000" class="mw-redirect" title="V2000">V2000</a> and many Hi-band formats – can keep mechanical jitter under control and assist <a href="Timebase_correction" class="mw-redirect" title="Timebase correction">timebase correction</a>.

</p><p>These FM systems are unusual, in that they have a ratio of carrier to maximum modulation frequency of less than two; contrast this with FM audio broadcasting, where the ratio is around 10,000. Consider, for example, a 6-MHz carrier modulated at a 3.5-MHz rate; by <a href="Bessel_function" title="Bessel function">Bessel</a> analysis, the first sidebands are on 9.5 and 2.5 MHz and the second sidebands are on 13 MHz and −1 MHz. The result is a reversed-phase sideband on +1 MHz; on demodulation, this results in unwanted output at 6 – 1 = 5 MHz. The system must be designed so that this unwanted output is reduced to an acceptable level.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading3"><h3 id="Sound">Sound</h3></div>

<p>FM is also used at <a href="Audio_frequency" title="Audio frequency">audio frequencies</a> to synthesize sound. This technique, known as <a href="Frequency_modulation_synthesis" title="Frequency modulation synthesis">FM synthesis</a>, was popularized by early digital <a href="Synthesizer" title="Synthesizer">synthesizers</a> and became a standard feature in several generations of <a href="Personal_computer" title="Personal computer">personal computer</a> <a href="Sound_card" title="Sound card">sound cards</a>.

</p>

<div class="mw-heading mw-heading3"><h3 id="Radio">Radio</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="FM_broadcasting" title="FM broadcasting">FM broadcasting</a></div>

<p><a href="Edwin_Howard_Armstrong" title="Edwin Howard Armstrong">Edwin Howard Armstrong</a> (1890–1954) was an American electrical engineer who invented wideband frequency modulation (FM) radio.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup>

He patented the regenerative circuit in 1914, the superheterodyne receiver in 1918 and the super-regenerative circuit in 1922.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> Armstrong presented his paper, "A Method of Reducing Disturbances in Radio Signaling by a System of Frequency Modulation", (which first described FM radio) before the New York section of the <a href="Institute_of_Radio_Engineers" title="Institute of Radio Engineers">Institute of Radio Engineers</a> on November 6, 1935. The paper was published in 1936.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup>

</p><p>As the name implies, wideband FM (WFM) requires a wider <a href="Signal_bandwidth" class="mw-redirect" title="Signal bandwidth">signal bandwidth</a> than <a href="Amplitude_modulation" title="Amplitude modulation">amplitude modulation</a> by an equivalent modulating signal; this also makes the signal more robust against <a href="Noise_(radio)" class="mw-redirect" title="Noise (radio)">noise</a> and <a href="Interference_(communication)" title="Interference (communication)">interference</a>. Frequency modulation is also more robust against signal-amplitude-fading phenomena. As a result, FM was chosen as the modulation standard for high frequency, <a href="High_fidelity" title="High fidelity">high fidelity</a> <a href="Radio" title="Radio">radio</a> transmission, hence the term "<a href="FM_radio" class="mw-redirect" title="FM radio">FM radio</a>" (although for many years the <a href="BBC" title="BBC">BBC</a> called it "VHF radio" because commercial FM broadcasting uses part of the <a href="VHF" class="mw-redirect" title="VHF">VHF</a> band – the <a href="FM_broadcast_band" title="FM broadcast band">FM broadcast band</a>). FM <a href="Receiver_(radio)" class="mw-redirect" title="Receiver (radio)">receivers</a> employ a special <a href="Detector_(radio)" title="Detector (radio)">detector</a> for FM signals and exhibit a phenomenon known as the <i><a href="Capture_effect" title="Capture effect">capture effect</a></i>, in which the <a href="Tuner_(radio)" title="Tuner (radio)">tuner</a> "captures" the stronger of two stations on the same frequency while rejecting the other (compare this with a similar situation on an AM receiver, where both stations can be heard simultaneously). <a href="Frequency_drift" title="Frequency drift">Frequency drift</a> or a lack of <a href="Selectivity_(radio)" title="Selectivity (radio)">selectivity</a> may cause one station to be overtaken by another on an <a href="Adjacent_channel" title="Adjacent channel">adjacent channel</a>. Frequency <a href="Drift_(telecommunication)" class="mw-redirect" title="Drift (telecommunication)">drift</a> was a problem in early (or inexpensive) receivers; inadequate selectivity may affect any tuner.

</p><p>A wideband FM signal can also be used to carry a <a href="Stereophonic_sound" title="Stereophonic sound">stereo</a> signal; this is done with <a href="Multiplexing" title="Multiplexing">multiplexing</a> and demultiplexing before and after the FM process. The FM modulation and demodulation process is identical in stereo and monaural processes.

</p><p>FM is commonly used at <a href="VHF" class="mw-redirect" title="VHF">VHF</a> <a href="Radio_frequencies" class="mw-redirect" title="Radio frequencies">radio frequencies</a> for <a href="High-fidelity" class="mw-redirect" title="High-fidelity">high-fidelity</a> <a href="Radio_broadcasting" title="Radio broadcasting">broadcasts</a> of music and <a href="Speech_communication" class="mw-redirect" title="Speech communication">speech</a>. In broadcast services, where audio fidelity is important, wideband FM is generally used. Analog TV sound is also broadcast using FM. Narrowband FM is used for voice communications in commercial and <a href="Amateur_radio" title="Amateur radio">amateur radio</a> settings. In <a href="Two-way_radio" title="Two-way radio">two-way radio</a>, narrowband FM (NBFM) is used to conserve bandwidth for land mobile, marine mobile and other radio services.

</p><p>A high-efficiency radio-frequency <a href="Switching_amplifier" class="mw-redirect" title="Switching amplifier">switching amplifier</a> can be used to transmit FM signals (and other <a href="Constant_envelope" title="Constant envelope">constant-amplitude signals</a>). For a given signal strength (measured at the receiver antenna), switching amplifiers use <a href="Low-power_electronics" title="Low-power electronics">less battery power</a> and typically cost less than a <a href="Linear_amplifier" title="Linear amplifier">linear amplifier</a>. This gives FM another advantage over other modulation methods requiring linear amplifiers, such as AM and <a href="Quadrature_amplitude_modulation" title="Quadrature amplitude modulation">QAM</a>.

</p><p>There are reports that on October 5, 1924, Professor <a href="Mikhail_A._Bonch-Bruevich" class="mw-redirect" title="Mikhail A. Bonch-Bruevich">Mikhail A. Bonch-Bruevich</a>, during a scientific and technical conversation in the <a href="Nizhny_Novgorod_Radio_Laboratory" title="Nizhny Novgorod Radio Laboratory">Nizhny Novgorod Radio Laboratory</a>, reported about his new method of telephony, based on a change in the period of oscillations. Demonstration of frequency modulation was carried out on the laboratory model.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading3"><h3 id="Hearing_assistive_technology">Hearing assistive technology</h3></div>

<p>Frequency modulated systems are a widespread and commercially available <a href="Assistive_technology" title="Assistive technology">assistive technology</a> that make speech more understandable by improving the signal-to-noise ratio in the user's ear. They are also called <i>auditory trainers</i>, a term which refers to any sound amplification system not classified as a <a href="Hearing_aid" title="Hearing aid">hearing aid</a>. They intensify signal levels from the source by 15 to 20 decibels.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> FM systems are used by hearing-impaired people as well as children whose listening is affected by disorders such as <a href="Auditory_processing_disorder" title="Auditory processing disorder">auditory processing disorder</a> or <a href="ADHD" class="mw-redirect" title="ADHD">ADHD</a>.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> For people with <a href="Sensorineural_hearing_loss" title="Sensorineural hearing loss">sensorineural hearing loss</a>, FM systems result in better speech perception than hearing aids. They can be coupled with behind-the-ear hearing aids to allow the user to alternate the setting.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> FM systems are more convenient and cost-effective than alternatives such as <a href="Cochlear_implants" class="mw-redirect" title="Cochlear implants">cochlear implants</a>, but many users use FM systems infrequently due to their conspicuousness and need for recharging.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup>

</p>

/* start https://en.wikipedia.org/ */

.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .infobox .side-box{font-size:100%}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}

/* end https://en.wikipedia.org/ */

</style><style data-mw-deduplicate="TemplateStyles:r1237033735">

/* start https://en.wikipedia.org/ */

@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}

/* end https://en.wikipedia.org/ */

</style><div class="side-box side-box-right sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">

/* start https://en.wikipedia.org/ */

.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}

/* end https://en.wikipedia.org/ */

</style>

<div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Frequency_modulation" class="extiw external" title="commons:Category:Frequency modulation">Frequency modulation</a></span>.</div></div>

</div>

<ul><li><a href="Continuous-wave_frequency-modulated_radar" class="mw-redirect" title="Continuous-wave frequency-modulated radar">Continuous-wave frequency-modulated radar</a></li>

<li><a href="Chirp" title="Chirp">Chirp</a></li>

<li><a href="FM_stereo" class="mw-redirect" title="FM stereo">FM stereo</a></li>

<li><a href="FM-UWB" title="FM-UWB">FM-UWB</a> (FM and Ultra Wideband)</li>

<li><a href="History_of_radio" title="History of radio">History of radio</a></li>

<li><a href="Modulation" class="mw-redirect" title="Modulation">Modulation</a>, for a list of other modulation techniques</li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

/* start https://en.wikipedia.org/ */

.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}

/* end https://en.wikipedia.org/ */

</style><div class="reflist reflist-columns references-column-width" style="column-width: 25em;">

/* start https://en.wikipedia.org/ */

.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("./mw/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("./mw/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("./mw/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("./mw/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}

/* end https://en.wikipedia.org/ */

</style><cite id="CITEREFSmith1993" class="citation book cs1">Smith, Robert H. (1993). <i>Machines and Inventions</i>. Alexandria, VA: Time Life. p. 85. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-8094-9704-2</bdi>.</cite></span>

</li>

<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite id="CITEREFGibilisco2002" class="citation book cs1">Gibilisco, Stan (2002). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/teachyourselfele00gibi"><i>Teach yourself electricity and electronics</i></a></span>. McGraw-Hill Professional. p. <a rel="nofollow" class="external text" href="https://archive.org/details/teachyourselfele00gibi/page/477">477</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-07-137730-0</bdi>. <q>morse-code frequency-shift-keying sent-using-fsk.</q></cite></span>

</li>

<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><cite id="CITEREFRutledge1999" class="citation book cs1">Rutledge, David B. (1999). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=ZvJYLhk4N64C&q=radio-teletype+fsk&pg=RA2-PA310"><i>The Electronics of Radio</i></a>. Cambridge University Press. p. 310. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-521-64645-1</bdi>.</cite></span>

</li>

<li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text">B. Boashash, editor, <i>Time-Frequency Signal Analysis and Processing – A Comprehensive Reference</i>, Elsevier Science, Oxford, 2003; <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-08-044335-4</bdi></span>

</li>

<li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><cite id="CITEREFFaruque2017" class="citation book cs1">Faruque, Saleh (2017). <a rel="nofollow" class="external text" href="https://nvhrbiblio.nl/biblio/boek/Faruque%20-%20Radio%20Frequency%20Modulation%20made%20easy.pdf"><i>Radio Frequency Modulation Made Easy</i></a> <span class="cs1-format">(PDF)</span>. Springer Cham. pp. <span class="nowrap">33–</span>37. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-319-41200-9</bdi>.</cite></span>

</li>

<li id="cite_note-TGTSCS05-6"><span class="mw-cite-backlink">^ <a href="#cite_ref-TGTSCS05_6-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-TGTSCS05_6-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">T.G. Thomas, S. C. Sekhar <i>Communication Theory</i>, Tata-McGraw Hill 2005, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-07-059091-5</bdi> p. 136</span>

</li>

<li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://ib-lenhardt.com/kb/glossary/frequency-modulation">"Frequency Modulation (FM): Basics and Applications"</a>. <i>IB-Lenhardt AG</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2025-07-16</span></span>.</cite></span>

</li>

<li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><cite id="CITEREFDer" class="citation web cs1">Der, Lawrence. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20141021093250/http://www.silabs.com/Marcom%20Documents/Resources/FMTutorial.pdf">"Frequency Modulation (FM) Tutorial"</a> <span class="cs1-format">(PDF)</span>. <i>Silicon Laboratories</i>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:48672999">48672999</a>. Archived from <a rel="nofollow" class="external text" href="http://www.silabs.com/Marcom%20Documents/Resources/FMTutorial.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2014-10-21<span class="reference-accessdate">. Retrieved <span class="nowrap">17 October</span> 2019</span>.</cite></span>

</li>

<li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text">Lathi, B. P. (1968). <i>Communication Systems</i>, pp. 214–17. New York: John Wiley and Sons, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-471-51832-8</bdi>.</span>

</li>

<li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><cite id="CITEREFH._P._Westman1970" class="citation book cs1">H. P. Westman, ed. (1970). <i>Reference Data for Radio Engineers</i> (Fifth ed.). Howard W. Sams & Co. pp. <span class="nowrap">21–</span>11.</cite></span>

</li>

<li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><cite id="CITEREFAlan_Bloom2010" class="citation book cs1">Alan Bloom (2010). "Chapter 8. Modulation". In H. Ward Silver; Mark J. Wilson (eds.). <i>The ARRL Handbook for Radio Communications</i>. American Radio Relay League. p. 8.7. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-87259-146-2</bdi>.</cite></span>

</li>

<li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text">Haykin, Simon [Ed]. (2001). <i>Communication Systems</i>, 4th ed.</span>

</li>

<li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><cite id="CITEREFShima1995" class="citation book cs1">Shima, James Michael (1995). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Aq7uygAACAAJ"><i>FM Demodulation Using a Digital Radio and Digital Signal Processing</i></a>. University of Florida.</cite></span>

</li>

<li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text">"FM Systems Of Exceptional Bandwidth" Proc. IEEE vol. 112, no. 9, p. 1664, September 1965</span>

</li>

<li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><cite id="CITEREFA._Michael_Noll2001" class="citation book cs1">A. Michael Noll (2001). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/principlesofmode0000noll"><i>Principles of modern communications technology</i></a></span>. Artech House. p. <a rel="nofollow" class="external text" href="https://archive.org/details/principlesofmode0000noll/page/104">104</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1580532846</bdi>.</cite></span>

</li>

/* start https://en.wikipedia.org/ */

.mw-parser-output .citation{word-wrap:break-word}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}

/* end https://en.wikipedia.org/ */

</style><span class="citation patent"><a rel="nofollow" class="external text" href="https://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=US1342885">US 1342885</a></span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Apatent&rft.number=1342885&rft.cc=US&rft.title="><span style="display: none;"> </span></span></span>

</li>

<li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><cite id="CITEREFArmstrong1936" class="citation journal cs1">Armstrong, E. H. (May 1936). "A Method of Reducing Disturbances in Radio Signaling by a System of Frequency Modulation". <i>Proceedings of the IRE</i>. <b>24</b> (5). IRE: <span class="nowrap">689–</span>740. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FJRPROC.1936.227383">10.1109/JRPROC.1936.227383</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:43628076">43628076</a>.</cite></span>

</li>

<li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text">Ф. Лбов. <a rel="nofollow" class="external text" href="https://sergeyhry.narod.ru/rl/rl1924_06_09.htm">Новая система радиофона</a> «Радиолюбитель». – 1924. – № 6. – С. 86.</span>

</li>

<li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"><cite id="CITEREFASHA_Ad_Hoc_Committee_on_FM_Systems2002" class="citation techreport cs1">ASHA Ad Hoc Committee on FM Systems (2002) [Original March 1994]. <a rel="nofollow" class="external text" href="https://www.asha.org/policy/gl2002-00010/"><i>Guidelines for Fitting and Monitoring FM Systems</i></a> (Technical report) (Revised ed.). <a href="American_Speech%E2%80%93Language%E2%80%93Hearing_Association" title="American Speech–Language–Hearing Association">American Speech–Language–Hearing Association</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1044%2Fpolicy.GL2002-00010">10.1044/policy.GL2002-00010</a>.</cite></span>

</li>

<li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><cite id="CITEREFSchaferBryantSandersBaldus2014" class="citation journal cs1">Schafer, Erin C.; Bryant, Danielle; Sanders, Katie; Baldus, Nicole; Algier, Katherine; Lewis, Audrey; Traber, Jordan; Layden, Paige; Amin, Aneeqa (June 1, 2014). "Fitting and Verification of Frequency Modulation on Children with Normal Hearing". <i>Journal of the American Academy of Audiology</i>. <b>25</b> (6): <span class="nowrap">529–</span>540. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.3766%2Fjaaa.25.6.3">10.3766/jaaa.25.6.3</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1050-0545">1050-0545</a>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/25313543">25313543</a>. <a href="EBSCOhost_(identifier)" class="mw-redirect" title="EBSCOhost (identifier)">EBSCO<i>host</i></a> <a rel="nofollow" class="external text" href="http://search.ebscohost.com/login.aspx?direct=true&AN=107832936">107832936</a> – via <a href="EBSCOhost" class="mw-redirect" title="EBSCOhost">EBSCOhost</a>.</cite></span>

</li>

<li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><cite id="CITEREFLewisCrandallValenteEnrietto_Horn2004" class="citation journal cs1">Lewis, M. Samantha; Crandall, Carl C.; Valente, Michael; Enrietto Horn, Jane (2004). <span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://digitalcommons.wustl.edu/audio_hapubs/5">"Speech perception in noise: directional microphones versus frequency modulation (FM) systems"</a></span>. <i>Journal of the American Academy of Audiology</i>. <b>15</b> (6): <span class="nowrap">426–</span>439. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.3766%2Fjaaa.15.6.4">10.3766/jaaa.15.6.4</a></span>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/15341224">15341224</a>.</cite></span>

</li>

<li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><cite id="CITEREFMcArdleAbramsHnath_Chisholm2005" class="citation journal cs1">McArdle, Rachel; Abrams, Harvey B.; Hnath Chisholm, Theresa (2005). "When Hearing Aids Go Bad: An FM Success Story". <i>Journal of the American Academy of Audiology</i>. <b>16</b> (10): <span class="nowrap">809–</span>821. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.3766%2Fjaaa.16.10.5">10.3766/jaaa.16.10.5</a>. <a href="EBSCOhost_(identifier)" class="mw-redirect" title="EBSCOhost (identifier)">EBSCO<i>host</i></a> <a rel="nofollow" class="external text" href="http://search.ebscohost.com/login.aspx?direct=true&AN=106441304">106441304</a> – via <a href="EBSCOhost" class="mw-redirect" title="EBSCOhost">EBSCOhost</a>.</cite></span>

</li>

</ol></div>

<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>

<ul><li><cite id="CITEREFCarlson2001" class="citation book cs1">Carlson, A. Bruce (2001). <i>Communication Systems</i>. Science/Engineering/Math (4th ed.). McGraw-Hill. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-07-011127-1</bdi>.</cite></li>

<li><cite id="CITEREFFrost2010" class="citation book cs1">Frost, Gary L. (2010). <i>Early FM Radio: Incremental technology in twentieth-century America</i>. Baltimore, MD: Johns Hopkins University Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-8018-9440-4</bdi>.</cite></li>

<li><cite id="CITEREFSeymour2005" class="citation book cs1">Seymour, Ken (2005) [1996]. "Frequency Modulation". <i>The Electronics Handbook</i> (2nd ed.). CRC Press. pp. <span class="nowrap">1188–</span>1200. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-8493-8345-5</bdi>.</cite></li></ul>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><a rel="nofollow" class="external text" href="https://colab.research.google.com/drive/14Ws9gX1hPzBkE7P1sBepVuoz-uo2f-Be?usp=sharing">Analog Modulation online interactive demonstration</a> using Python in <a rel="nofollow" class="external text" href="https://colab.research.google.com">Google Colab Platform</a>, by C Foh.</li></ul>

/* start https://en.wikipedia.org/ */

.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}

/* end https://en.wikipedia.org/ */

</style></div><div role="navigation" class="navbox" aria-labelledby="Analog_television_broadcasting_topics253" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Analog_television_broadcasting_topics253" style="font-size:114%;margin:0 4em"><a href="Analog_television" title="Analog television">Analog television</a> <a href="Outline_of_television_broadcasting" title="Outline of television broadcasting">broadcasting topics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Broadcast_television_systems" title="Broadcast television systems">Systems</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="405-line_television_system" title="405-line television system">405-line</a> (<a href="CCIR_System_A" title="CCIR System A">System A</a>)</li>

<li><a href="525-line_television_system" class="mw-redirect" title="525-line television system">525-line</a> (<a href="CCIR_System_M" title="CCIR System M">System M</a>)</li>

<li><a href="625-line_television_system" class="mw-redirect" title="625-line television system">625-line</a> (<a href="CCIR_System_B" title="CCIR System B">System B</a>, <a href="CCIR_System_C" title="CCIR System C">System C</a>, <a href="CCIR_System_D" title="CCIR System D">System D</a>, <a href="CCIR_System_G" title="CCIR System G">System G</a>, <a href="CCIR_System_H" title="CCIR System H">System H</a>, <a href="CCIR_System_I" title="CCIR System I">System I</a>, <a href="CCIR_System_K" title="CCIR System K">System K</a>, <a href="CCIR_System_L" title="CCIR System L">System L</a>, <a href="CCIR_System_N" title="CCIR System N">System N</a>)</li>

<li><a href="819_line" title="819 line">819-line</a> (<a href="CCIR_System_E" title="CCIR System E">System E</a>, <a href="CCIR_System_F" title="CCIR System F">System F</a>)</li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Color systems</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="Clear-Vision" title="Clear-Vision">Clear-Vision</a></li>

<li><a href="PALplus" title="PALplus">PALplus</a></li>

<li><a href="SECAM" title="SECAM">SECAM</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Video</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Analog_television#Structure_of_a_video_signal" title="Analog television">Back porch</a> and <a href="Analog_television#Structure_of_a_video_signal" title="Analog television">front porch</a></li>

<li><a href="Black_level" title="Black level">Black level</a></li>

<li><a href="Blanking_level" title="Blanking level">Blanking level</a></li>

<li><a href="Chrominance" title="Chrominance">Chrominance</a></li>

<li><a href="Chrominance_subcarrier" title="Chrominance subcarrier">Chrominance subcarrier</a></li>

<li><a href="Colorburst" title="Colorburst">Colorburst</a></li>

<li><a href="Color_killer" title="Color killer">Color killer</a></li>

<li><a href="Color_television" title="Color television">Color TV</a></li>

<li><a href="Composite_video" title="Composite video">Composite video</a></li>

<li><a href="Frame_(video)" class="mw-redirect" title="Frame (video)">Frame (video)</a></li>

<li><a href="Horizontal_scan_rate" title="Horizontal scan rate">Horizontal scan rate</a></li>

<li><a href="Horizontal_blanking_interval" title="Horizontal blanking interval">Horizontal blanking interval</a></li>

<li><a href="Nominal_analogue_blanking" title="Nominal analogue blanking">Nominal analogue blanking</a></li>

<li><a href="Overscan" title="Overscan">Overscan</a></li>

<li><a href="Raster_scan" title="Raster scan">Raster scan</a></li>

<li><a href="Television_lines" title="Television lines">Television lines</a></li>

<li><a href="Vertical_blanking_interval" title="Vertical blanking interval">Vertical blanking interval</a></li>

<li><a href="White_clipper" title="White clipper">White clipper</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Sound</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Multichannel_Television_Sound" title="Multichannel Television Sound">Multichannel Television Sound</a></li>

<li><a href="NICAM" title="NICAM">NICAM</a></li>

<li><a href="Sound-in-Syncs" title="Sound-in-Syncs">Sound-in-Syncs</a></li>

<li><a href="Zweikanalton" title="Zweikanalton">Zweikanalton</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Modulation</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul>

<li><a href="Quadrature_amplitude_modulation" title="Quadrature amplitude modulation">Quadrature amplitude modulation</a></li>

<li><a href="Single-sideband_modulation#Vestigial_sideband_(VSB)" title="Single-sideband modulation">Vestigial sideband modulation (VSB)</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Transmission</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Amplifier#Electronic_amplifiers" title="Amplifier">Amplifiers</a></li>

<li><a href="Antenna_(radio)" title="Antenna (radio)">Antenna (radio)</a></li>

<li><a href="Broadcast_transmitter" title="Broadcast transmitter">Broadcast transmitter</a>/<a href="Transmitter_station" title="Transmitter station">Transmitter station</a></li>

<li><a href="Resonator#Electromagnetic" title="Resonator">Cavity amplifier</a></li>

<li><a href="Differential_gain" title="Differential gain">Differential gain</a></li>

<li><a href="Differential_phase" title="Differential phase">Differential phase</a></li>

<li><a href="Diplexer" title="Diplexer">Diplexer</a></li>

<li><a href="Dipole_antenna" title="Dipole antenna">Dipole antenna</a></li>

<li><a href="Dummy_load" title="Dummy load">Dummy load</a></li>

<li><a href="Frequency_mixer" title="Frequency mixer">Frequency mixer</a></li>

<li><a href="Intercarrier_method" title="Intercarrier method">Intercarrier method</a></li>

<li><a href="Intermediate_frequency" title="Intermediate frequency">Intermediate frequency</a></li>

<li><a href="Output_power_of_an_analog_TV_transmitter" title="Output power of an analog TV transmitter">Output power of an analog TV transmitter</a></li>

<li><a href="Pre-emphasis" class="mw-redirect" title="Pre-emphasis">Pre-emphasis</a></li>

<li><a href="Residual_carrier" title="Residual carrier">Residual carrier</a></li>

<li><a href="Split_sound_system" title="Split sound system">Split sound system</a></li>

<li><a href="Superheterodyne_transmitter" title="Superheterodyne transmitter">Superheterodyne transmitter</a></li>

<li><a href="Television_receive-only" title="Television receive-only">Television receive-only</a></li>

<li><a href="Direct-broadcast_satellite_television" class="mw-redirect" title="Direct-broadcast satellite television">Direct-broadcast satellite television</a></li>

<li><a href="Television_transmitter" title="Television transmitter">Television transmitter</a></li>

<li><a href="Terrestrial_television" title="Terrestrial television">Terrestrial television</a></li>

<li><a href="Transposer" title="Transposer">Transposer</a></li>

<li><a href="Digital_television_transition" title="Digital television transition">Digital television transition</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Radio_frequency" title="Radio frequency">Frequencies</a> & bands</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Frequency_offset" title="Frequency offset">Frequency offset</a></li>

<li><a href="Microwave_transmission" title="Microwave transmission">Microwave transmission</a></li>

<li><a href="Television_channel_frequencies" title="Television channel frequencies">Television channel frequencies</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Radio_propagation" title="Radio propagation">Propagation</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="Distortion" title="Distortion">Distortion</a></li>

<li><a href="Earth_bulge" class="mw-redirect" title="Earth bulge">Earth bulge</a></li>

<li><a href="Field_strength_in_free_space" class="mw-redirect" title="Field strength in free space">Field strength in free space</a></li>

<li><a href="Noise_(electronics)" title="Noise (electronics)">Noise (electronics)</a></li>

<li><a href="Radiation_pattern" title="Radiation pattern">Radiation pattern</a></li>

<li><a href="Television_interference" title="Television interference">Television interference</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Testing</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Distortionmeter" title="Distortionmeter">Distortionmeter</a></li>

<li><a href="Field_strength_meter" title="Field strength meter">Field strength meter</a></li>

<li><a href="Vectorscope" title="Vectorscope">Vectorscope</a></li>

<li><a href="VIT_signals" title="VIT signals">VIT signals</a></li>

<li><a href="Zero_reference_pulse" title="Zero reference pulse">Zero reference pulse</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Artifacts</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Dot_crawl" title="Dot crawl">Dot crawl</a></li>

<li><a href="Ghosting_(television)" title="Ghosting (television)">Ghosting</a></li>

<li><a href="Hanover_bars" title="Hanover bars">Hanover bars</a></li>

<li><a href="Sparklies" title="Sparklies">Sparklies</a></li></ul>

</div></td></tr></tbody></table></div>

<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Telecommunications802" style="padding:3px"><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Telecommunications802" style="font-size:114%;margin:0 4em"><a href="Telecommunications" title="Telecommunications">Telecommunications</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="History_of_telecommunication" title="History of telecommunication">History</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Beacon#For_defensive_communications" title="Beacon">Beacon</a></li>

<li><a href="History_of_broadcasting" title="History of broadcasting">Broadcasting</a></li>

<li><a href="Cable_protection_system" title="Cable protection system">Cable protection system</a></li>

<li><a href="Cable_television" title="Cable television">Cable TV</a></li>

<li><a href="Communications_satellite#History" title="Communications satellite">Communications satellite</a></li>

<li><a href="Computer_network#History" title="Computer network">Computer network</a></li>

<li><a href="Data_compression" title="Data compression">Data compression</a>

<ul><li><a href="Audio_coding_format" title="Audio coding format">audio</a></li>

<li><a href="Image_compression" title="Image compression">image</a></li>

<li><a href="Video_coding_format" title="Video coding format">video</a></li></ul></li>

<li><a href="Digital_media" title="Digital media">Digital media</a>

<ul><li><a href="Internet_video" title="Internet video">Internet video</a></li>

<li><a href="Online_video_platform" title="Online video platform">online video platform</a></li>

<li><a href="Social_media" title="Social media">social media</a></li>

<li><a href="Streaming_media" title="Streaming media">streaming</a></li></ul></li>

<li><a href="Drums_in_communication" title="Drums in communication">Drums</a></li>

<li><a href="Edholm's_law" title="Edholm's law">Edholm's law</a></li>

<li><a href="Electrical_telegraph#History" title="Electrical telegraph">Electrical telegraph</a></li>

<li><a href="Heliograph#History" title="Heliograph">Heliographs</a></li>

<li><a href="Hydraulic_telegraph#Greek_hydraulic_semaphore_system" title="Hydraulic telegraph">Hydraulic telegraph</a></li>

<li><a href="Information_Age" title="Information Age">Information Age</a></li>

<li><a href="Information_revolution" class="mw-redirect" title="Information revolution">Information revolution</a></li>

<li><a href="History_of_the_Internet" title="History of the Internet">Internet</a></li>

<li><a href="Mass_media#History" title="Mass media">Mass media</a></li>

<li><a href="History_of_mobile_phones" title="History of mobile phones">Mobile phone</a>

<ul><li><a href="Smartphone" title="Smartphone">Smartphone</a></li></ul></li>

<li><a href="Optical_communication" title="Optical communication">Optical telecommunication</a></li>

<li><a href="Optical_telegraph" title="Optical telegraph">Optical telegraphy</a></li>

<li><a href="Pager" title="Pager">Pager</a></li>

<li><a href="Photophone" title="Photophone">Photophone</a></li>

<li><a href="History_of_prepaid_mobile_phones" title="History of prepaid mobile phones">Prepaid mobile phone</a></li>

<li><a href="History_of_radio" title="History of radio">Radio</a></li>

<li><a href="Radiotelephone" title="Radiotelephone">Radiotelephone</a></li>

<li><a href="Communications_satellite" title="Communications satellite">Satellite communications</a></li>

<li><a href="Semaphore" title="Semaphore">Semaphore</a>

<ul><li><a href="Phryctoria" title="Phryctoria">Phryctoria</a></li></ul></li>

<li><a href="Semiconductor" title="Semiconductor">Semiconductor</a>

<ul><li><a href="Semiconductor_device" title="Semiconductor device">device</a></li>

<li><a href="MOSFET" title="MOSFET">MOSFET</a></li>

<li><a href="History_of_the_transistor" title="History of the transistor">transistor</a></li></ul></li>

<li><a href="Smoke_signal" title="Smoke signal">Smoke signals</a></li>

<li><a href="History_of_telecommunication" title="History of telecommunication">Telecommunications history</a></li>

<li><a href="Telautograph" title="Telautograph">Telautograph</a></li>

<li><a href="Telegraphy" title="Telegraphy">Telegraphy</a></li>

<li><a href="Teleprinter" title="Teleprinter">Teleprinter</a> (teletype)</li>

<li><a href="History_of_the_telephone" title="History of the telephone">Telephone</a></li>

<li><i><a href="The_Telephone_Cases" title="The Telephone Cases">The Telephone Cases</a></i></li>

<li><a href="History_of_television" title="History of television">Television</a>

<ul><li><a href="Digital_television" title="Digital television">digital</a></li>

<li><a href="Streaming_television" title="Streaming television">streaming</a></li></ul></li>

<li><a href="Submarine_communications_cable#Early_history:_telegraph_and_coaxial_cables" title="Submarine communications cable">Undersea telegraph line</a></li>

<li><a href="History_of_videotelephony" title="History of videotelephony">Videotelephony</a></li>

<li><a href="Whistled_language" title="Whistled language">Whistled language</a></li>

<li><a href="Wireless_revolution" class="mw-redirect" title="Wireless revolution">Wireless revolution</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Pioneers</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Nasir_Ahmed_(engineer)" title="Nasir Ahmed (engineer)">Nasir Ahmed</a></li>

<li><a href="Edwin_Howard_Armstrong" title="Edwin Howard Armstrong">Edwin Howard Armstrong</a></li>

<li><a href="Mohamed_M._Atalla" title="Mohamed M. Atalla">Mohamed M. Atalla</a></li>

<li><a href="John_Logie_Baird" title="John Logie Baird">John Logie Baird</a></li>

<li><a href="Paul_Baran" title="Paul Baran">Paul Baran</a></li>

<li><a href="John_Bardeen" title="John Bardeen">John Bardeen</a></li>

<li><a href="Alexander_Graham_Bell" title="Alexander Graham Bell">Alexander Graham Bell</a></li>

<li><a href="Emile_Berliner" title="Emile Berliner">Emile Berliner</a></li>

<li><a href="Tim_Berners-Lee" title="Tim Berners-Lee">Tim Berners-Lee</a></li>

<li><a href="Francis_Blake_(inventor)" title="Francis Blake (inventor)">Francis Blake</a></li>

<li><a href="Jagadish_Chandra_Bose" title="Jagadish Chandra Bose">Jagadish Chandra Bose</a></li>

<li><a href="Charles_Bourseul" title="Charles Bourseul">Charles Bourseul</a></li>

<li><a href="Walter_Houser_Brattain" class="mw-redirect" title="Walter Houser Brattain">Walter Houser Brattain</a></li>

<li><a href="Claude_Chappe" title="Claude Chappe">Claude Chappe</a></li>

<li><a href="Yogen_Dalal" class="mw-redirect" title="Yogen Dalal">Yogen Dalal</a></li>

<li><a href="Donald_Davies" title="Donald Davies">Donald Davies</a></li>

<li><a href="Daniel_Davis_Jr." title="Daniel Davis Jr.">Daniel Davis Jr.</a></li>

<li><a href="Amos_Dolbear" title="Amos Dolbear">Amos Dolbear</a></li>

<li><a href="Thomas_Edison" title="Thomas Edison">Thomas Edison</a></li>

<li><a href="Philo_Farnsworth" title="Philo Farnsworth">Philo Farnsworth</a></li>

<li><a href="Reginald_Fessenden" title="Reginald Fessenden">Reginald Fessenden</a></li>

<li><a href="Lee_de_Forest" title="Lee de Forest">Lee de Forest</a></li>

<li><a href="Elisha_Gray" title="Elisha Gray">Elisha Gray</a></li>

<li><a href="Oliver_Heaviside" title="Oliver Heaviside">Oliver Heaviside</a></li>

<li><a href="Robert_Hooke" title="Robert Hooke">Robert Hooke</a></li>

<li><a href="Erna_Schneider_Hoover" title="Erna Schneider Hoover">Erna Schneider Hoover</a></li>

<li><a href="Harold_Hopkins_(physicist)" title="Harold Hopkins (physicist)">Harold Hopkins</a></li>

<li><a href="Gardiner_Greene_Hubbard" title="Gardiner Greene Hubbard">Gardiner Greene Hubbard</a></li>

<li><a href="Dawon_Kahng" title="Dawon Kahng">Dawon Kahng</a></li>

<li><a href="Charles_K._Kao" title="Charles K. Kao">Charles K. Kao</a></li>

<li><a href="Narinder_Singh_Kapany" title="Narinder Singh Kapany">Narinder Singh Kapany</a></li>

<li><a href="Hedy_Lamarr" title="Hedy Lamarr">Hedy Lamarr</a></li>

<li><a href="Roberto_Landell_de_Moura" title="Roberto Landell de Moura">Roberto Landell</a></li>

<li><a href="Innocenzo_Manzetti" title="Innocenzo Manzetti">Innocenzo Manzetti</a></li>

<li><a href="Guglielmo_Marconi" title="Guglielmo Marconi">Guglielmo Marconi</a></li>

<li><a href="Robert_Metcalfe" title="Robert Metcalfe">Robert Metcalfe</a></li>

<li><a href="Antonio_Meucci" title="Antonio Meucci">Antonio Meucci</a></li>

<li><a href="Samuel_Morse" title="Samuel Morse">Samuel Morse</a></li>

<li><a href="Jun-ichi_Nishizawa" title="Jun-ichi Nishizawa">Jun-ichi Nishizawa</a></li>

<li><a href="Charles_Grafton_Page" title="Charles Grafton Page">Charles Grafton Page</a></li>

<li><a href="Radia_Perlman" title="Radia Perlman">Radia Perlman</a></li>

<li><a href="Alexander_Stepanovich_Popov" class="mw-redirect" title="Alexander Stepanovich Popov">Alexander Stepanovich Popov</a></li>

<li><a href="Tivadar_Pusk%C3%A1s" title="Tivadar Puskás">Tivadar Puskás</a></li>

<li><a href="Johann_Philipp_Reis" title="Johann Philipp Reis">Johann Philipp Reis</a></li>

<li><a href="Claude_Shannon" title="Claude Shannon">Claude Shannon</a></li>

<li><a href="Almon_Brown_Strowger" title="Almon Brown Strowger">Almon Brown Strowger</a></li>

<li><a href="Henry_Sutton_(inventor)" title="Henry Sutton (inventor)">Henry Sutton</a></li>

<li><a href="Charles_Sumner_Tainter" title="Charles Sumner Tainter">Charles Sumner Tainter</a></li>

<li><a href="Nikola_Tesla" title="Nikola Tesla">Nikola Tesla</a></li>

<li><a href="Camille_Tissot" title="Camille Tissot">Camille Tissot</a></li>

<li><a href="Alfred_Vail" title="Alfred Vail">Alfred Vail</a></li>

<li><a href="Thomas_A._Watson" title="Thomas A. Watson">Thomas A. Watson</a></li>

<li><a href="Charles_Wheatstone" title="Charles Wheatstone">Charles Wheatstone</a></li>

<li><a href="Vladimir_K._Zworykin" title="Vladimir K. Zworykin">Vladimir K. Zworykin</a></li>

<li><i><a href="List_of_Internet_pioneers" title="List of Internet pioneers">Internet pioneers</a></i></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Transmission_medium" title="Transmission medium">Transmission<br>media</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Coaxial_cable" title="Coaxial cable">Coaxial cable</a></li>

<li><a href="Fiber-optic_communication" title="Fiber-optic communication">Fiber-optic communication</a>

<ul><li><a href="Optical_fiber" title="Optical fiber">optical fiber</a></li></ul></li>

<li><a href="Free-space_optical_communication" title="Free-space optical communication">Free-space optical communication</a></li>

<li><a href="Molecular_communication" title="Molecular communication">Molecular communication</a></li>

<li><a href="Radio_wave" title="Radio wave">Radio waves</a>

<ul><li><a href="Wireless" title="Wireless">wireless</a></li></ul></li>

<li><a href="Transmission_line" title="Transmission line">Transmission line</a>

<ul><li><a href="Telecommunication_circuit" title="Telecommunication circuit">telecommunication circuit</a></li></ul></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Network_topology" title="Network topology">Network topology</a><br>and switching</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Bandwidth_(computing)" title="Bandwidth (computing)">Bandwidth</a></li>

<li><a href="Telecommunications_link" title="Telecommunications link">Links</a></li>

<li><a href="Network_switch" title="Network switch">Network switching</a>

<ul><li><a href="Circuit_switching" title="Circuit switching">circuit</a></li>

<li><a href="Packet_switching" title="Packet switching">packet</a></li></ul></li>

<li><a href="Node_(networking)" title="Node (networking)">Nodes</a>

<ul><li><a href="Terminal_(telecommunication)" title="Terminal (telecommunication)">terminal</a></li></ul></li>

<li><a href="Telephone_exchange" title="Telephone exchange">Telephone exchange</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Multiplexing" title="Multiplexing">Multiplexing</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Space-division_multiple_access" title="Space-division multiple access">Space-division</a></li>

<li><a href="Frequency-division_multiplexing" title="Frequency-division multiplexing">Frequency-division</a></li>

<li><a href="Time-division_multiplexing" title="Time-division multiplexing">Time-division</a></li>

<li><a href="Polarization-division_multiplexing" title="Polarization-division multiplexing">Polarization-division</a></li>

<li><a href="Orbital_angular_momentum_multiplexing" title="Orbital angular momentum multiplexing">Orbital angular-momentum</a></li>

<li><a href="Code-division_multiple_access" title="Code-division multiple access">Code-division</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Communication_protocol" title="Communication protocol">Communication protocol</a></li>

<li><a href="Computer_network" title="Computer network">Computer network</a></li>

<li><a href="Data_communication" title="Data communication">Data transmission</a></li>

<li><a href="Store_and_forward" title="Store and forward">Store and forward</a></li>

<li><a href="Telecommunications_equipment" title="Telecommunications equipment">Telecommunications equipment</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Telecommunications_network" title="Telecommunications network">Types of network</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Cellular_network" title="Cellular network">Cellular network</a></li>

<li><a href="Ethernet" title="Ethernet">Ethernet</a></li>

<li><a href="Mobile_telephony" title="Mobile telephony">Mobile</a></li>

<li><a href="Public_switched_telephone_network" title="Public switched telephone network">Public Switched Telephone</a></li>

<li><a href="Radio_network" title="Radio network">Radio</a></li>

<li><a href="Television_broadcasting" class="mw-redirect" title="Television broadcasting">Television</a></li>

<li><a href="Telex" title="Telex">Telex</a></li>

<li><a href="Wireless_network" title="Wireless network">Wireless network</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Telecommunications_network" title="Telecommunications network">Notable networks</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="ARPANET" title="ARPANET">ARPANET</a></li>

<li><a href="BITNET" title="BITNET">BITNET</a></li>

<li><a href="CYCLADES" title="CYCLADES">CYCLADES</a></li>

<li><a href="FidoNet" title="FidoNet">FidoNet</a></li>

<li><a href="Internet" title="Internet">Internet</a></li>

<li><a href="Internet2" title="Internet2">Internet2</a></li>

<li><a href="JANET" title="JANET">JANET</a></li>

<li><a href="NPL_network" title="NPL network">NPL network</a></li>

<li><a href="TANet" title="TANet">TANet</a></li>

<li><a href="Toasternet" title="Toasternet">Toasternet</a></li>

<li><a href="Usenet" title="Usenet">Usenet</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Locations</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li>Africa</li>

<li>Americas

<ul><li>North</li>

<li>South</li></ul></li>

<li>Antarctica</li>

<li>Europe</li>

<li>Oceania</li>

<li><i><a href="List_of_telecommunications_regulatory_bodies" title="List of telecommunications regulatory bodies">Global telecommunications regulation bodies</a></i></li></ul>

</div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div>

<ul><li><span class="nowrap"><span class="noviewer" typeof="mw:File"><span></span></span> </span><a href="Portal%3ATelecommunication" title="Portal:Telecommunication">Telecommunication portal</a></li>

<li><span class="noviewer" typeof="mw:File"><span title="Category"></span></span> Category</li>

<li><span class="noviewer" typeof="mw:File"><span title="List-Class article"></span></span> <a href="Outline_of_telecommunication" title="Outline of telecommunication">Outline</a></li>

<li><span class="noviewer" typeof="mw:File"><span title="Commons page"></span></span> <a href="https://commons.wikimedia.org/wiki/Category:Telecommunications" class="extiw external" title="commons:Category:Telecommunications">Commons</a></li></ul>

</div></td></tr></tbody></table></div>

<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Analog_and_digital_audio_broadcasting130" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Analog_and_digital_audio_broadcasting130" style="font-size:114%;margin:0 4em"><a href="Analog_recording" title="Analog recording">Analog</a> and <a href="Digital_audio" title="Digital audio">digital audio</a> <a href="Broadcasting" title="Broadcasting">broadcasting</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Terrestrial</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Radio" title="Radio">Radio</a> <a href="Modulation" class="mw-redirect" title="Modulation">modulation</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="Orthogonal_frequency-division_multiplexing" title="Orthogonal frequency-division multiplexing">COFDM</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Frequency_allocation" title="Frequency allocation">Frequency allocations</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Digital systems</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="FMeXtra" title="FMeXtra">FMeXtra</a></li>

<li><a href="HD_Radio" title="HD Radio">HD Radio</a></li>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Satellite</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Frequency allocations</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Digital systems</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Commercial_broadcasting" title="Commercial broadcasting">Commercial radio</a> providers</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="SiriusXM" title="SiriusXM">SiriusXM</a>

<ul><li><a href="SiriusXM_Canada" title="SiriusXM Canada">Canada</a></li></ul></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Audio_codec" title="Audio codec">Codecs</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="MPEG-1_Audio_Layer_II" title="MPEG-1 Audio Layer II">MPEG-1 Audio Layer II</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Subcarrier" title="Subcarrier">Subcarrier</a> signals</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="DirectBand" title="DirectBand">DirectBand</a></li>

</div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Related_topics252" style="font-size:114%;margin:0 4em">Related topics</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Technical (audio)</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Audio_data_compression" class="mw-redirect" title="Audio data compression">Audio data compression</a></li>

<li><a href="Audio_signal_processing" title="Audio signal processing">Audio signal processing</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Technical (<a href="AM_stereo" title="AM stereo">AM stereo</a> formats)</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="AM_stereo#Belar_System" title="AM stereo">Belar</a></li>

<li><a href="AM_stereo#Harris_System" title="AM stereo">Harris</a></li>

<li><a href="AM_stereo#Kahn-Hazeltine" title="AM stereo">Kahn-Hazeltine</a></li>

<li><a href="AM_stereo#Magnavox_System" title="AM stereo">Magnavox</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Technical (emission)</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="AM_broadcasting" title="AM broadcasting">AM broadcasting</a></li>

<li><a href="AM_expanded_band" title="AM expanded band">AM expanded band</a></li>

<li><a href="Cable_radio" title="Cable radio">Cable radio</a></li>

<li><a href="Digital_radio" title="Digital radio">Digital radio</a></li>

<li><a href="Error_detection_and_correction" title="Error detection and correction">Error detection and correction</a></li>

<li><a href="FM_broadcast_band" title="FM broadcast band">FM broadcast band</a></li>

<li><a href="FM_broadcasting" title="FM broadcasting">FM broadcasting</a></li>

<li><a href="FM_extended_band_in_Brazil" title="FM extended band in Brazil">FM extended band in Brazil</a></li>

<li><a href="Multipath_propagation" title="Multipath propagation">Multipath propagation</a></li>

<li><a href="Shortwave_relay_station" title="Shortwave relay station">Shortwave relay station</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Cultural</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="History_of_radio" title="History of radio">History of radio</a></li>

<li><a href="International_broadcasting" title="International broadcasting">International broadcasting</a></li></ul>

</div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div>

<ul><li><b><span class="nowrap"><span class="noviewer" typeof="mw:File"><span></span></span> </span><a href="Portal%3ARadio" title="Portal:Radio">Radio portal</a></b></li>

<li><a href="Comparison_of_radio_systems" title="Comparison of radio systems">Comparison of radio systems</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr></tbody></table></div>

/* start https://en.wikipedia.org/ */

.mw-parser-output .tooltip-dotted{border-bottom:1px dotted;cursor:help}

/* end https://en.wikipedia.org/ */

</style></div><div role="navigation" class="navbox authority-control" aria-labelledby="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q181417#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata1194" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q181417#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata1194" style="font-size:114%;margin:0 4em">Authority control databases </div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">National</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4155410-3">Germany</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh85110474">United States</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Modulation de fréquence"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb11950829t">France</a></span></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Modulation de fréquence"><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb11950829t">BnF data</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.nli.org.il/en/authorities/987007558365005171">Israel</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://lux.collections.yale.edu/view/concept/b800ced5-7f2d-4ea4-ab5f-f071aaacb490">Yale LUX</a></span></li></ul></div></td></tr></tbody></table></div></div><div><div class="zim-footer">

This article is issued from <a class="external text" title="Last edited on 2025-07-16" href="https://en.wikipedia.org/wiki/?title=Frequency_modulation&oldid=1300855958">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

</div>

</div></div>

</div>

</main>

</div>

</body></html>