SherbyNet - /page/wikibook/entry.mu

Micron Document

<!DOCTYPE html>

<title>Signal processing</title>

</head>

<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Signal processing</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">"Signal theory" redirects here; not to be confused with <a href="Signalling_theory" title="Signalling theory">Signalling theory</a> or <a href="Signalling_(economics)" title="Signalling (economics)">Signalling (economics)</a>.</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><style data-mw-deduplicate="TemplateStyles:r1248332772">

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

.mw-parser-output .multiple-issues-text{width:95%;margin:0.2em 0}.mw-parser-output .multiple-issues-text>.mw-collapsible-content{margin-top:0.3em}.mw-parser-output .compact-ambox .ambox{border:none;border-collapse:collapse;background-color:transparent;margin:0 0 0 1.6em!important;padding:0!important;width:auto;display:block}body.mediawiki .mw-parser-output .compact-ambox .ambox.mbox-small-left{font-size:100%;width:auto;margin:0}.mw-parser-output .compact-ambox .ambox .mbox-text{padding:0!important;margin:0!important}.mw-parser-output .compact-ambox .ambox .mbox-text-span{display:list-item;line-height:1.5em;list-style-type:disc}body.skin-minerva .mw-parser-output .multiple-issues-text>.mw-collapsible-toggle,.mw-parser-output .compact-ambox .ambox .mbox-image,.mw-parser-output .compact-ambox .ambox .mbox-imageright,.mw-parser-output .compact-ambox .ambox .mbox-empty-cell,.mw-parser-output .compact-ambox .hide-when-compact{display:none}

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

</style>

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

.mw-parser-output .tmulti .multiimageinner{display:flex;flex-direction:column}.mw-parser-output .tmulti .trow{display:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box}.mw-parser-output .tmulti .tsingle{margin:1px;float:left}.mw-parser-output .tmulti .theader{clear:both;font-weight:bold;text-align:center;align-self:center;background-color:transparent;width:100%}.mw-parser-output .tmulti .thumbcaption{background-color:transparent}.mw-parser-output .tmulti .text-align-left{text-align:left}.mw-parser-output .tmulti .text-align-right{text-align:right}.mw-parser-output .tmulti .text-align-center{text-align:center}@media all and (max-width:720px){.mw-parser-output .tmulti .thumbinner{width:100%!important;box-sizing:border-box;max-width:none!important;align-items:center}.mw-parser-output .tmulti .trow{justify-content:center}.mw-parser-output .tmulti .tsingle{float:none!important;max-width:100%!important;box-sizing:border-box;text-align:center}.mw-parser-output .tmulti .tsingle .thumbcaption{text-align:left}.mw-parser-output .tmulti .trow>.thumbcaption{text-align:center}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmulti .multiimageinner span:not(.skin-invert-image):not(.skin-invert):not(.bg-transparent) img{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmulti .multiimageinner span:not(.skin-invert-image):not(.skin-invert):not(.bg-transparent) img{background-color:white}}

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

</style><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:408px;max-width:408px"><div class="trow"><div class="tsingle" style="width:202px;max-width:202px"><div class="thumbimage"><span typeof="mw:File"><span></span></span></div></div><div class="tsingle" style="width:202px;max-width:202px"><div class="thumbimage"><span typeof="mw:File"><span></span></span></div></div></div><div class="trow" style="display:flex"><div class="thumbcaption">The signal on the left looks like noise, but the signal processing technique known as <a href="Spectral_density_estimation" title="Spectral density estimation">spectral density estimation</a> (right) shows that it contains five well-defined frequency components.</div></div></div></div>

<p><b>Signal processing</b> is an <a href="Electrical_engineering" title="Electrical engineering">electrical engineering</a> subfield that focuses on analyzing, modifying and synthesizing <i><a href="Signal" title="Signal">signals</a></i>, such as <a href="Audio_signal_processing" title="Audio signal processing">sound</a>, <a href="Image_processing" class="mw-redirect" title="Image processing">images</a>, <a href="Scalar_potential" title="Scalar potential">potential fields</a>, <a href="Seismic_tomography" title="Seismic tomography">seismic signals</a>, <a href="Altimeter" title="Altimeter">altimetry processing</a>, and <a href="Scientific_measurements" class="mw-redirect" title="Scientific measurements">scientific measurements</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> Signal processing techniques are used to optimize transmissions, <a href="Data_storage" title="Data storage">digital storage</a> efficiency, correcting distorted signals, improve <a href="Subjective_video_quality" title="Subjective video quality">subjective video quality</a>, and to detect or pinpoint components of interest in a measured signal.<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>

</p>

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

<p>According to <a href="Alan_V._Oppenheim" title="Alan V. Oppenheim">Alan V. Oppenheim</a> and <a href="Ronald_W._Schafer" title="Ronald W. Schafer">Ronald W. Schafer</a>, the principles of signal processing can be found in the classical <a href="Numerical_analysis" title="Numerical analysis">numerical analysis</a> techniques of the 17th century. They further state that the digital refinement of these techniques can be found in the digital <a href="Control_system" title="Control system">control systems</a> of the 1940s and 1950s.<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>In 1948, <a href="Claude_Shannon" title="Claude Shannon">Claude Shannon</a> wrote the influential paper "<a href="A_Mathematical_Theory_of_Communication" title="A Mathematical Theory of Communication">A Mathematical Theory of Communication</a>" which was published in the <i><a href="Bell_System_Technical_Journal" class="mw-redirect" title="Bell System Technical Journal">Bell System Technical Journal</a></i>.<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> The paper laid the groundwork for later development of information communication systems and the processing of signals for transmission.<sup id="cite_ref-fifty_5-0" class="reference"><a href="#cite_note-fifty-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>

</p><p>Signal processing matured and flourished in the 1960s and 1970s, and <a href="Digital_signal_processing" title="Digital signal processing">digital signal processing</a> became widely used with specialized <a href="Digital_signal_processor" title="Digital signal processor">digital signal processor</a> chips in the 1980s.<sup id="cite_ref-fifty_5-1" class="reference"><a href="#cite_note-fifty-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading2"><h2 id="Definition_of_a_signal">Definition of a signal</h2></div>

<p>A signal is a <a href="Function_(mathematics)" title="Function (mathematics)">function</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 x(t)}">

</mstyle>

</mrow>

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

</semantics>

</p>

<ul><li>deterministic (then one speaks of a deterministic signal) or</li>

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

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

</semantics>

</math></span><img src="./6f1396498f56d9580f5b1625df064d63e84ab5b8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.044ex; height:2.843ex;" alt="{\displaystyle (x_{t})_{t\in T}}" loading="lazy"></span>, a realization of a <a href="Stochastic_process" title="Stochastic process">stochastic process</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 (X_{t})_{t\in T}}">

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle (X_{t})_{t\in T}}</annotation>

</semantics>

</math></span><img src="./f05f8b9d621c0c80afa86a7198ba021247d3a40a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.639ex; height:2.843ex;" alt="{\displaystyle (X_{t})_{t\in T}}" loading="lazy"></span></li></ul>

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

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

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Analog_signal_processing" title="Analog signal processing">Analog signal processing</a></div>

<p>Analog signal processing is for signals that have not been digitized, as in most 20th-century <a href="Radio" title="Radio">radio</a>, telephone, and television systems. This involves linear electronic circuits as well as nonlinear ones. The former are, for instance, <a href="Passive_filter" class="mw-redirect" title="Passive filter">passive filters</a>, <a href="Active_filter" title="Active filter">active filters</a>, <a href="Electronic_mixer" title="Electronic mixer">additive mixers</a>, <a href="Integrator" title="Integrator">integrators</a>, and <a href="Analog_delay_line" title="Analog delay line">delay lines</a>. Nonlinear circuits include <a href="Compandor" class="mw-redirect" title="Compandor">compandors</a>, multipliers (<a href="Frequency_mixer" title="Frequency mixer">frequency mixers</a>, <a href="Voltage-controlled_amplifier" class="mw-redirect" title="Voltage-controlled amplifier">voltage-controlled amplifiers</a>), <a href="Voltage-controlled_filter" title="Voltage-controlled filter">voltage-controlled filters</a>, <a href="Voltage-controlled_oscillator" title="Voltage-controlled oscillator">voltage-controlled oscillators</a>, and <a href="Phase-locked_loop" title="Phase-locked loop">phase-locked loops</a>.

</p>

<div class="mw-heading mw-heading3"><h3 id="Continuous_time">Continuous time</h3></div>

<p><a href="Continuous_signal" class="mw-redirect" title="Continuous signal">Continuous-time signal</a> processing is for signals that vary with the change of continuous domain (without considering some individual interrupted points).

</p><p>The methods of signal processing include <a href="Time_domain" title="Time domain">time domain</a>, <a href="Frequency_domain" title="Frequency domain">frequency domain</a>, and <a href="Complex_frequency" class="mw-redirect" title="Complex frequency">complex frequency domain</a>. This technology mainly discusses the modeling of a <a href="Linear_time-invariant" class="mw-redirect" title="Linear time-invariant">linear time-invariant</a> continuous system, integral of the system's zero-state response, setting up system function and the continuous time filtering of deterministic signals. For example, in time domain, a continuous-time 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(t)}">

</mstyle>

</mrow>

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

</semantics>

</math></span><img src="./d54c275db3a1e620737b58e143b0818107fa5f5c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.979ex; height:2.843ex;" alt="{\displaystyle x(t)}" loading="lazy"></span> passing through a <a href="Linear_time-invariant" class="mw-redirect" title="Linear time-invariant">linear time-invariant</a> filter/system denoted as <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(t)}">

</mstyle>

</mrow>

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

</semantics>

</p><p><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 y(t)=\int _{-\infty }^{\infty }h(\tau )x(t-\tau )\,d\tau }">

</mrow>

</mrow>

</msubsup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle y(t)=\int _{-\infty }^{\infty }h(\tau )x(t-\tau )\,d\tau }</annotation>

</semantics>

</math></span><img src="./f7346d6decd983238af39e135de7ee4ab334a31b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:26.912ex; height:6.009ex;" alt="{\displaystyle y(t)=\int _{-\infty }^{\infty }h(\tau )x(t-\tau )\,d\tau }" loading="lazy"></span>

</p><p>In some contexts, <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(t)}">

</mstyle>

</mrow>

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

</semantics>

</math></span><img src="./66abbb8ae1d9f30bb529739b109e1e5bbe83c626.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.988ex; height:2.843ex;" alt="{\displaystyle h(t)}" loading="lazy"></span> is referred to as the impulse response of the system. The above <a href="Convolution" title="Convolution">convolution</a> operation is conducted between the input and the system.

</p>

<div class="mw-heading mw-heading3"><h3 id="Discrete_time">Discrete time</h3></div>

<p><a href="Discrete-time_signal" class="mw-redirect" title="Discrete-time signal">Discrete-time signal</a> processing is for sampled signals, defined only at discrete points in time, and as such are quantized in time, but not in magnitude.

</p><p><i>Analog discrete-time signal processing</i> is a technology based on electronic devices such as <a href="Sample_and_hold" title="Sample and hold">sample and hold</a> circuits, analog time-division <a href="Multiplexer" title="Multiplexer">multiplexers</a>, <a href="Analog_delay_line" title="Analog delay line">analog delay lines</a> and <a href="Analog_feedback_shift_register" title="Analog feedback shift register">analog feedback shift registers</a>. This technology was a predecessor of digital signal processing (see below), and is still used in advanced processing of gigahertz signals.<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>The concept of discrete-time signal processing also refers to a theoretical discipline that establishes a mathematical basis for digital signal processing, without taking <a href="Quantization_error" class="mw-redirect" title="Quantization error">quantization error</a> into consideration.

</p>

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

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Digital_signal_processing" title="Digital signal processing">Digital signal processing</a></div>

<p>Digital signal processing is the processing of digitized discrete-time sampled signals. Processing is done by general-purpose <a href="Computer" title="Computer">computers</a> or by digital circuits such as <a href="ASIC" class="mw-redirect" title="ASIC">ASICs</a>, <a href="Field-programmable_gate_array" title="Field-programmable gate array">field-programmable gate arrays</a> or specialized <a href="Digital_signal_processor" title="Digital signal processor">digital signal processors</a>. Typical arithmetical operations include <a href="Fixed-point_arithmetic" title="Fixed-point arithmetic">fixed-point</a> and <a href="Floating-point" class="mw-redirect" title="Floating-point">floating-point</a>, real-valued and complex-valued, multiplication and addition. Other typical operations supported by the hardware are <a href="Circular_buffer" title="Circular buffer">circular buffers</a> and <a href="Lookup_table" title="Lookup table">lookup tables</a>. Examples of algorithms are the <a href="Fast_Fourier_transform" title="Fast Fourier transform">fast Fourier transform</a> (FFT), <a href="Finite_impulse_response" title="Finite impulse response">finite impulse response</a> (FIR) filter, <a href="Infinite_impulse_response" title="Infinite impulse response">Infinite impulse response</a> (IIR) filter, and <a href="Adaptive_filter" title="Adaptive filter">adaptive filters</a> such as the <a href="Wiener_filter" title="Wiener filter">Wiener</a> and <a href="Kalman_filter" title="Kalman filter">Kalman filters</a>.

</p>

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

<p>Nonlinear signal processing involves the analysis and processing of signals produced from <a href="Nonlinear_system" title="Nonlinear system">nonlinear systems</a> and can be in the time, <a href="Frequency" title="Frequency">frequency</a>, or spatiotemporal domains.<sup id="cite_ref-Billings_8-0" class="reference"><a href="#cite_note-Billings-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-VSA_9-0" class="reference"><a href="#cite_note-VSA-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Nonlinear systems can produce highly complex behaviors including <a href="Bifurcation_theory" title="Bifurcation theory">bifurcations</a>, <a href="Chaos_theory" title="Chaos theory">chaos</a>, <a href="Harmonics" class="mw-redirect" title="Harmonics">harmonics</a>, and <a href="Subharmonics" class="mw-redirect" title="Subharmonics">subharmonics</a> which cannot be produced or analyzed using linear methods.

</p><p>Polynomial signal processing is a type of non-linear signal processing, where <a href="Polynomial" title="Polynomial">polynomial</a> systems may be interpreted as conceptually straightforward extensions of linear systems to the nonlinear case.<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>

</p>

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

<p><b>Statistical signal processing</b> is an approach which treats signals as <a href="Stochastic_process" title="Stochastic process">stochastic processes</a>, utilizing their <a href="Statistical" class="mw-redirect" title="Statistical">statistical</a> properties to perform signal processing tasks.<sup id="cite_ref-Scharf_11-0" class="reference"><a href="#cite_note-Scharf-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> Statistical techniques are widely used in signal processing applications. For example, one can model the <a href="Probability_distribution" title="Probability distribution">probability distribution</a> of noise incurred when photographing an image, and construct techniques based on this model to <a href="Noise_reduction" title="Noise reduction">reduce the noise</a> in the resulting image.

</p>

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

<p><b>Graph signal processing</b> generalizes signal processing tasks to signals living on non-Euclidean domains whose structure can be captured by a weighted graph.<sup id="cite_ref-Ortega_12-0" class="reference"><a href="#cite_note-Ortega-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> Graph signal processing presents several key points such as sampling signal techniques,<sup id="cite_ref-Tanaka_13-0" class="reference"><a href="#cite_note-Tanaka-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> recovery techniques <sup id="cite_ref-Fascista_14-0" class="reference"><a href="#cite_note-Fascista-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> and time-varying techiques.<sup id="cite_ref-Giraldo_15-0" class="reference"><a href="#cite_note-Giraldo-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> Graph signal processing has been applied with success in the field of image processing, computer vision <sup id="cite_ref-Giraldo1_16-0" class="reference"><a href="#cite_note-Giraldo1-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup>

<sup id="cite_ref-Giraldo3_18-0" class="reference"><a href="#cite_note-Giraldo3-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> and sound anomaly detection.<sup id="cite_ref-Bouwmans1_19-0" class="reference"><a href="#cite_note-Bouwmans1-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading2"><h2 id="Application_fields">Application fields</h2></div>

<ul><li><a href="Audio_signal_processing" title="Audio signal processing">Audio signal processing</a> – for electrical signals representing sound, such as <a href="Speech_signal_processing" class="mw-redirect" title="Speech signal processing">speech</a> or music<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></li>

<li><a href="Image_processing" class="mw-redirect" title="Image processing">Image processing</a> – in digital cameras, computers and various imaging systems</li>

<li><a href="Video_processing" title="Video processing">Video processing</a> – for interpreting moving pictures</li>

<li><a href="Wireless_communication" class="mw-redirect" title="Wireless communication">Wireless communication</a> – waveform generations, demodulation, filtering, equalization</li>

<li><a href="Control_systems" class="mw-redirect" title="Control systems">Control systems</a></li>

<li><a href="Array_processing" title="Array processing">Array processing</a> – for processing signals from arrays of sensors</li>

<li><a href="Process_control" class="mw-redirect" title="Process control">Process control</a> – a variety of signals are used, including the industry standard <a href="4-20_mA_current_loop" class="mw-redirect" title="4-20 mA current loop">4-20 mA current loop</a></li>

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

<li><a href="Feature_extraction" class="mw-redirect" title="Feature extraction">Feature extraction</a>, such as <a href="Image_understanding" class="mw-redirect" title="Image understanding">image understanding</a>, <a href="Semantic_audio" title="Semantic audio">semantic audio</a> and <a href="Speech_recognition" title="Speech recognition">speech recognition</a>.</li>

<li>Quality improvement, such as <a href="Noise_reduction" title="Noise reduction">noise reduction</a>, <a href="Image_enhancement" class="mw-redirect" title="Image enhancement">image enhancement</a>, and <a href="Echo_cancellation" class="mw-redirect" title="Echo cancellation">echo cancellation</a>.</li>

<li>Source coding including <a href="Audio_compression_(data)" class="mw-redirect" title="Audio compression (data)">audio compression</a>, <a href="Image_compression" title="Image compression">image compression</a>, and <a href="Video_compression" class="mw-redirect" title="Video compression">video compression</a>.</li>

<li><a href="Genomic" class="mw-redirect" title="Genomic">Genomic</a> signal processing<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></li>

<li>In <a href="Geophysics" title="Geophysics">geophysics</a>, signal processing is used to amplify the signal vs the noise within <a href="Time-series" class="mw-redirect" title="Time-series">time-series</a> measurements of geophysical data. Processing is conducted within the <a href="Time_domain" title="Time domain">time domain</a> or <a href="Frequency_domain" title="Frequency domain">frequency domain</a>, or both.<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><sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup></li></ul>

<p>In communication systems, signal processing may occur at:

</p>

<ul><li>OSI layer 1 in the seven-layer <a href="OSI_model" title="OSI model">OSI model</a>, the <a href="Physical_layer" title="Physical layer">physical layer</a> (<a href="Modulation" class="mw-redirect" title="Modulation">modulation</a>, <a href="Equalization_(communications)" title="Equalization (communications)">equalization</a>, <a href="Multiplexing" title="Multiplexing">multiplexing</a>, etc.);</li>

<li>OSI layer 2, the <a href="Data_link_layer" title="Data link layer">data link layer</a> (<a href="Forward_error_correction" class="mw-redirect" title="Forward error correction">forward error correction</a>);</li>

<li>OSI layer 6, the <a href="Presentation_layer" title="Presentation layer">presentation layer</a> (source coding, including <a href="Analog-to-digital_conversion" class="mw-redirect" title="Analog-to-digital conversion">analog-to-digital conversion</a> and <a href="Data_compression" title="Data compression">data compression</a>).</li></ul>

<div class="mw-heading mw-heading2"><h2 id="Typical_devices">Typical devices</h2></div>

<ul><li><a href="Filter_(signal_processing)" title="Filter (signal processing)">Filters</a> – for example analog (passive or active) or digital (<a href="FIR_filter" class="mw-redirect" title="FIR filter">FIR</a>, <a href="IIR_filter" class="mw-redirect" title="IIR filter">IIR</a>, frequency domain or <a href="Stochastic_filter" class="mw-redirect" title="Stochastic filter">stochastic filters</a>, etc.)</li>

<li><a href="Sampling_(signal_processing)" title="Sampling (signal processing)">Samplers</a> and <a href="Analog-to-digital_converter" title="Analog-to-digital converter">analog-to-digital converters</a> for <a href="Signal_acquisition" class="mw-redirect" title="Signal acquisition">signal acquisition</a> and reconstruction, which involves measuring a physical signal, storing or transferring it as digital signal, and possibly later rebuilding the original signal or an approximation thereof.</li>

<li><a href="Digital_signal_processor" title="Digital signal processor">Digital signal processors</a> (DSPs)</li></ul>

<div class="mw-heading mw-heading2"><h2 id="Mathematical_methods_applied">Mathematical methods applied</h2></div>

<ul><li><a href="Differential_equations" class="mw-redirect" title="Differential equations">Differential equations</a><sup id="cite_ref-Gaydecki2004_24-0" class="reference"><a href="#cite_note-Gaydecki2004-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> – for modeling system behavior, connecting input and output relations in linear time-invariant systems. For instance, a low-pass filter such as an <a href="RC_circuit" title="RC circuit">RC circuit</a> can be modeled as a differential equation in signal processing, which allows one to compute the continuous output signal as a function of the input or initial conditions.</li>

<li><a href="Recurrence_relation" title="Recurrence relation">Recurrence relations</a><sup id="cite_ref-Engelberg2008_25-0" class="reference"><a href="#cite_note-Engelberg2008-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup></li>

<li><a href="Transform_theory" title="Transform theory">Transform theory</a></li>

<li><a href="Time-frequency_analysis" class="mw-redirect" title="Time-frequency analysis">Time-frequency analysis</a> – for processing non-stationary signals<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup></li>

<li><a href="Linear_canonical_transformation" title="Linear canonical transformation">Linear canonical transformation</a></li>

<li><a href="Spectral_estimation" class="mw-redirect" title="Spectral estimation">Spectral estimation</a> – for determining the spectral content (i.e., the distribution of power over frequency) of a set of <a href="Time_series" title="Time series">time series</a> data points<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup></li>

<li><a href="Statistical_signal_processing" class="mw-redirect" title="Statistical signal processing">Statistical signal processing</a> – analyzing and extracting information from signals and noise based on their stochastic properties</li>

<li><a href="Linear_time-invariant_system" title="Linear time-invariant system">Linear time-invariant system</a> theory, and <a href="Transform_theory" title="Transform theory">transform theory</a></li>

<li><a href="Polynomial_signal_processing" class="mw-redirect" title="Polynomial signal processing">Polynomial signal processing</a> – analysis of systems which relate input and output using polynomials</li>

<li><a href="System_identification" title="System identification">System identification</a><sup id="cite_ref-Billings_8-1" class="reference"><a href="#cite_note-Billings-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> and classification</li>

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

<li><a href="Coding_theory" title="Coding theory">Coding theory</a></li>

<li><a href="Complex_analysis" title="Complex analysis">Complex analysis</a><sup id="cite_ref-SchreierScharf2010_28-0" class="reference"><a href="#cite_note-SchreierScharf2010-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup></li>

<li><a href="Vector_spaces" class="mw-redirect" title="Vector spaces">Vector spaces</a> and <a href="Linear_algebra" title="Linear algebra">Linear algebra</a><sup id="cite_ref-Little2019_29-0" class="reference"><a href="#cite_note-Little2019-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup></li>

<li><a href="Functional_analysis" title="Functional analysis">Functional analysis</a><sup id="cite_ref-DamelinJr2012_30-0" class="reference"><a href="#cite_note-DamelinJr2012-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup></li>

<li><a href="Probability" title="Probability">Probability</a> and <a href="Stochastic_processes" class="mw-redirect" title="Stochastic processes">stochastic processes</a><sup id="cite_ref-Scharf_11-1" class="reference"><a href="#cite_note-Scharf-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup></li>

<li><a href="Detection_theory" title="Detection theory">Detection theory</a></li>

<li><a href="Estimation_theory" title="Estimation theory">Estimation theory</a></li>

<li><a href="Optimization" class="mw-redirect" title="Optimization">Optimization</a><sup id="cite_ref-PalomarEldar2010_31-0" class="reference"><a href="#cite_note-PalomarEldar2010-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup></li>

<li><a href="Numerical_methods" class="mw-redirect" title="Numerical methods">Numerical methods</a></li>

<li><a href="Data_mining" title="Data mining">Data mining</a> – for statistical analysis of relations between large quantities of variables (in this context representing many physical signals), to extract previously unknown interesting patterns</li></ul>

<ul><li><a href="Algebraic_signal_processing" title="Algebraic signal processing">Algebraic signal processing</a></li>

<li><a href="Audio_filter" title="Audio filter">Audio filter</a></li>

<li><a href="Bounded_variation" title="Bounded variation">Bounded variation</a></li>

<li><a href="Dynamic_range_compression" title="Dynamic range compression">Dynamic range compression</a></li>

<li><a href="Information_theory" title="Information theory">Information theory</a></li>

<li><a href="Least-squares_spectral_analysis" title="Least-squares spectral analysis">Least-squares spectral analysis</a></li>

<li><a href="Non-local_means" title="Non-local means">Non-local means</a></li>

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

<li><a href="Sensitivity_(electronics)" title="Sensitivity (electronics)">Sensitivity (electronics)</a></li>

<li><a href="Similarity_(signal_processing)" title="Similarity (signal processing)">Similarity (signal processing)</a></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">

/* 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="CITEREFSenguptaSahidullah,_MdSaha,_Goutam2016" class="citation journal cs1">Sengupta, Nandini; Sahidullah, Md; Saha, Goutam (August 2016). "Lung sound classification using cepstral-based statistical features". <i>Computers in Biology and Medicine</i>. <b>75</b> (1): <span class="nowrap">118–</span>129. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.compbiomed.2016.05.013">10.1016/j.compbiomed.2016.05.013</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/27286184">27286184</a>.</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="CITEREFAlan_V._Oppenheim_and_Ronald_W._Schafer1989" class="citation book cs1">Alan V. Oppenheim and Ronald W. Schafer (1989). <i>Discrete-Time Signal Processing</i>. Prentice Hall. p. 1. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-13-216771-9</bdi>.</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="CITEREFOppenheim,_Alan_V.Schafer,_Ronald_W.1975" class="citation book cs1">Oppenheim, Alan V.; Schafer, Ronald W. (1975). <i>Digital Signal Processing</i>. <a href="Prentice_Hall" title="Prentice Hall">Prentice Hall</a>. p. 5. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-13-214635-5</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"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.computerhistory.org/revolution/digital-logic/12/269/1331">"A Mathematical Theory of Communication – CHM Revolution"</a>. <i>Computer History</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2019-05-13</span></span>.</cite></span>

</li>

<li id="cite_note-fifty-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-fifty_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-fifty_5-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><cite class="citation book cs1"><a rel="nofollow" class="external text" href="https://signalprocessingsociety.org/uploads/history/history.pdf"><i>Fifty Years of Signal Processing: The IEEE Signal Processing Society and its Technologies, 1948–1998</i></a> <span class="cs1-format">(PDF)</span>. The IEEE Signal Processing Society. 1998.</cite></span>

</li>

<li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text">Berber, S. (2021). Discrete Communication Systems. United Kingdom: Oxford University Press., page 9, <a rel="nofollow" class="external free" href="https://books.google.com/books?id=CCs0EAAAQBAJ&pg=PA9">https://books.google.com/books?id=CCs0EAAAQBAJ&pg=PA9</a></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://microwavelab.nd.edu/research/analog-signal-processing/">"Microwave & Millimeter-wave Circuits and Systems"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2024-10-20</span></span>.</cite></span>

</li>

<li id="cite_note-Billings-8"><span class="mw-cite-backlink">^ <a href="#cite_ref-Billings_8-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Billings_8-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><cite id="CITEREFBillings2013" class="citation book cs1">Billings, S. A. (2013). <i>Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains</i>. Wiley. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-119-94359-4</bdi>.</cite></span>

</li>

<li id="cite_note-VSA-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-VSA_9-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFSlawinska,_J.Ourmazd,_A.Giannakis,_D.2018" class="citation book cs1">Slawinska, J.; Ourmazd, A.; Giannakis, D. (2018). "A New Approach to Signal Processing of Spatiotemporal Data". <i>2018 IEEE Statistical Signal Processing Workshop (SSP)</i>. IEEE Xplore. pp. <span class="nowrap">338–</span>342. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FSSP.2018.8450704">10.1109/SSP.2018.8450704</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-5386-1571-3</bdi>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:52153144">52153144</a>.</cite></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="CITEREFV._John_MathewsGiovanni_L._Sicuranza2000" class="citation book cs1">V. John Mathews; Giovanni L. Sicuranza (May 2000). <i>Polynomial Signal Processing</i>. Wiley. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-471-03414-8</bdi>.</cite></span>

</li>

<li id="cite_note-Scharf-11"><span class="mw-cite-backlink">^ <a href="#cite_ref-Scharf_11-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Scharf_11-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><cite id="CITEREFScharf1991" class="citation book cs1">Scharf, Louis L. (1991). <i>Statistical signal processing: detection, estimation, and time series analysis</i>. <a href="Boston" title="Boston">Boston</a>: <a href="Addison%E2%80%93Wesley" class="mw-redirect" title="Addison–Wesley">Addison–Wesley</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-201-19038-9</bdi>. <a href="OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/61160161">61160161</a>.</cite></span>

</li>

<li id="cite_note-Ortega-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-Ortega_12-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFOrtega2022" class="citation book cs1">Ortega, A. (2022). <i>Introduction to Graph Signal Processing</i>. <a href="Cambridge" title="Cambridge">Cambridge</a>: <a href="Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9781108552349</bdi>.</cite></span>

</li>

<li id="cite_note-Tanaka-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-Tanaka_13-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFTanakaEldar2020" class="citation journal cs1">Tanaka, Y.; Eldar, Y. (2020). <a rel="nofollow" class="external text" href="https://ieeexplore.ieee.org/document/9043719">"Generalized Sampling on Graphs with Subspace and Smoothness Prior"</a>. <i>IEEE Transactions on Signal Processing</i>. <b>68</b>: <span class="nowrap">2272–</span>2286. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1905.04441">1905.04441</a></span>. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2020ITSP...68.2272T">2020ITSP...68.2272T</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FTSP.2020.2982325">10.1109/TSP.2020.2982325</a>.</cite></span>

</li>

<li id="cite_note-Fascista-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-Fascista_14-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFFascistaColucciaRavazzi2024" class="citation journal cs1">Fascista, A.; Coluccia, A.; Ravazzi, C. (2024). <span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://ieeexplore.ieee.org/document/10465260">"Graph Signal Reconstruction under Heterogeneous Noise via Adaptive Uncertainty-Aware Sampling and Soft Classification"</a></span>. <i>IEEE Transactions on Signal and Information Processing over Networks</i>. <b>10</b>: <span class="nowrap">277–</span>293. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FTSIPN.2024.3375593">10.1109/TSIPN.2024.3375593</a>.</cite></span>

</li>

<li id="cite_note-Giraldo-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-Giraldo_15-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFGiraldoMahmoodGarcia-GarciaThanou2022" class="citation journal cs1">Giraldo, J.; Mahmood, A.; Garcia-Garcia, B.; Thanou, D.; Bouwmans, T. (March 2022). <a rel="nofollow" class="external text" href="https://ieeexplore.ieee.org/document/9730033">"Reconstruction of Time-varying Graph Signals via Sobolev Smoothness"</a>. <i>IEEE Transactions on Signal and Information Processing over Networks</i>. <b>8</b>: <span class="nowrap">201–</span>214. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/2207.06439">2207.06439</a></span>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FTSIPN.2022.3156886">10.1109/TSIPN.2022.3156886</a>.</cite></span>

</li>

<li id="cite_note-Giraldo1-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-Giraldo1_16-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFGiraldoBouwmans2020" class="citation book cs1">Giraldo, J.; Bouwmans, T. (October 2020). <a rel="nofollow" class="external text" href="https://ieeexplore.ieee.org/document/9190887">"Semi-Supervised Background Subtraction of Unseen Videos: Minimization of the Total Variation of Graph Signals"</a>. <i>2020 IEEE International Conference on Image Processing (ICIP)</i>. pp. <span class="nowrap">3224–</span>3228. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FICIP40778.2020.9190887">10.1109/ICIP40778.2020.9190887</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-7281-6395-6</bdi>.</cite></span>

</li>

<li id="cite_note-Giraldo2-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-Giraldo2_17-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFGiraldoBouwmans2020" class="citation book cs1">Giraldo, J.; Bouwmans, T. (2020). <a rel="nofollow" class="external text" href="https://ieeexplore.ieee.org/document/9412999">"GraphBGS: Background Subtraction via Recovery of Graph Signals"</a>. <i>2020 25th International Conference on Pattern Recognition (ICPR)</i>. pp. <span class="nowrap">6881–</span>6888. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/2001.06404">2001.06404</a></span>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FICPR48806.2021.9412999">10.1109/ICPR48806.2021.9412999</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-7281-8808-9</bdi>.</cite></span>

</li>

<li id="cite_note-Giraldo3-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-Giraldo3_18-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFGiraldoJavedSultanaJung2021" class="citation book cs1">Giraldo, J.; Javed, S.; Sultana, M.; Jung, S.; Bouwmans, T. (February 2021). <a rel="nofollow" class="external text" href="https://link.springer.com/chapter/10.1007/978-3-030-81638-4_3">"The Emerging Field of Graph Signal Processing for Moving Object Segmentation"</a>. <i>Frontiers of Computer Vision</i>. Communications in Computer and Information Science. Vol. 1405. pp. <span class="nowrap">31–</span>45. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-030-81638-4_3">10.1007/978-3-030-81638-4_3</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-030-81637-7</bdi>.</cite></span>

</li>

<li id="cite_note-Bouwmans1-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-Bouwmans1_19-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFMnasriGiraldoBouwmans2024" class="citation journal cs1">Mnasri, Z.; Giraldo, H.; Bouwmans, T. (2024). <a rel="nofollow" class="external text" href="https://ieeexplore.ieee.org/document/10715291">"Anomalous Sound Detection for Road Surveillance based on Graph Signal Processing"</a>. <i>European Conference on Signal Processing, EUSIPCO 2024</i>: <span class="nowrap">161–</span>165. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.23919%2FEUSIPCO63174.2024.10715291">10.23919/EUSIPCO63174.2024.10715291</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-9-4645-9361-7</bdi>.</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="CITEREFSarangiSahidullah,_MdSaha,_Goutam2020" class="citation journal cs1">Sarangi, Susanta; Sahidullah, Md; Saha, Goutam (September 2020). "Optimization of data-driven filterbank for automatic speaker verification". <i>Digital Signal Processing</i>. <b>104</b>: 102795. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/2007.10729">2007.10729</a></span>. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2020DSP...10402795S">2020DSP...10402795S</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.dsp.2020.102795">10.1016/j.dsp.2020.102795</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:220665533">220665533</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="CITEREFAnastassiou2001" class="citation journal cs1">Anastassiou, D. (2001). "Genomic signal processing". <i>IEEE Signal Processing Magazine</i>. <b>18</b> (4). IEEE: <span class="nowrap">8–</span>20. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2001ISPM...18....8A">2001ISPM...18....8A</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2F79.939833">10.1109/79.939833</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="CITEREFTelfordGeldartSheriff1990" class="citation book cs1">Telford, William Murray; Geldart, L. P.; Sheriff, Robert E. (1990). <i>Applied geophysics</i>. <a href="Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-521-33938-4</bdi>.</cite></span>

</li>

<li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><cite id="CITEREFReynolds2011" class="citation book cs1">Reynolds, John M. (2011). <i>An Introduction to Applied and Environmental Geophysics</i>. <a href="Wiley-Blackwell" title="Wiley-Blackwell">Wiley-Blackwell</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-471-48535-3</bdi>.</cite></span>

</li>

<li id="cite_note-Gaydecki2004-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-Gaydecki2004_24-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFPatrick_Gaydecki2004" class="citation book cs1">Patrick Gaydecki (2004). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=6Qo7NvX3vz4C&q=%22differential+equation%22+OR+%22differential+equations%22&pg=PA40"><i>Foundations of Digital Signal Processing: Theory, Algorithms and Hardware Design</i></a>. IET. pp. 40–. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-85296-431-6</bdi>.</cite></span>

</li>

<li id="cite_note-Engelberg2008-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-Engelberg2008_25-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFShlomo_Engelberg2008" class="citation book cs1">Shlomo Engelberg (8 January 2008). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=z3CpcCHbtgIC"><i>Digital Signal Processing: An Experimental Approach</i></a>. Springer Science & Business Media. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-84800-119-0</bdi>.</cite></span>

</li>

<li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text"><cite id="CITEREFBoashash,_Boualem2003" class="citation book cs1">Boashash, Boualem, ed. (2003). <i>Time frequency signal analysis and processing a comprehensive reference</i> (1 ed.). Amsterdam: Elsevier. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-08-044335-4</bdi>.</cite></span>

</li>

<li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text"><cite id="CITEREFStoicaMoses2005" class="citation book cs1">Stoica, Petre; Moses, Randolph (2005). <a rel="nofollow" class="external text" href="http://user.it.uu.se/%7Eps/SAS-new.pdf"><i>Spectral Analysis of Signals</i></a> <span class="cs1-format">(PDF)</span>. NJ: Prentice Hall.</cite></span>

</li>

<li id="cite_note-SchreierScharf2010-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-SchreierScharf2010_28-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFPeter_J._SchreierLouis_L._Scharf2010" class="citation book cs1">Peter J. Schreier; Louis L. Scharf (4 February 2010). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=HBaxLfDsAHoC&q=%22complex+analysis%22"><i>Statistical Signal Processing of Complex-Valued Data: The Theory of Improper and Noncircular Signals</i></a>. Cambridge University Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-139-48762-7</bdi>.</cite></span>

</li>

<li id="cite_note-Little2019-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-Little2019_29-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFMax_A._Little2019" class="citation book cs1">Max A. Little (13 August 2019). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=ejGoDwAAQBAJ&q=%22vector+space%22"><i>Machine Learning for Signal Processing: Data Science, Algorithms, and Computational Statistics</i></a>. OUP Oxford. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-19-102431-3</bdi>.</cite></span>

</li>

<li id="cite_note-DamelinJr2012-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-DamelinJr2012_30-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFSteven_B._DamelinWillard_Miller,_Jr2012" class="citation book cs1">Steven B. Damelin; Willard Miller, Jr (2012). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=MtPLYXQ9d9MC&q=%22functional+analysis%22"><i>The Mathematics of Signal Processing</i></a>. Cambridge University Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-107-01322-3</bdi>.</cite></span>

</li>

<li id="cite_note-PalomarEldar2010-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-PalomarEldar2010_31-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFDaniel_P._PalomarYonina_C._Eldar2010" class="citation book cs1">Daniel P. Palomar; Yonina C. Eldar (2010). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=UOpnvPJ151gC"><i>Convex Optimization in Signal Processing and Communications</i></a>. Cambridge University Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-521-76222-9</bdi>.</cite></span>

</li>

</ol></div></div>

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

<ul><li><cite id="CITEREFByrne2014" class="citation book cs1">Byrne, Charles (2014). <a rel="nofollow" class="external text" href="https://www.taylorfrancis.com/books/oa-mono/10.1201/b17672/signal-processing-charles-byrne"><i>Signal Processing: A Mathematical Approach</i></a>. <a href="Taylor_%26_Francis" title="Taylor & Francis">Taylor & Francis</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1201%2Fb17672">10.1201/b17672</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9780429158711</bdi>.</cite></li>

<li><cite id="CITEREFP_Stoica2005" class="citation book cs1">P Stoica, R Moses (2005). <a rel="nofollow" class="external text" href="https://user.it.uu.se/%7Eps/SAS-new.pdf"><i>Spectral Analysis of Signals</i></a> <span class="cs1-format">(PDF)</span>. NJ: Prentice Hall.</cite></li>

<li><cite id="CITEREFPapoulis1991" class="citation book cs1">Papoulis, Athanasios (1991). <i>Probability, Random Variables, and Stochastic Processes</i> (third ed.). McGraw-Hill. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-07-100870-5</bdi>.</cite></li>

<li>Kainam Thomas Wong <a rel="nofollow" class="external autonumber" href="http://www.eie.polyu.edu.hk/~enktwong/">[1]</a>: Statistical Signal Processing lecture notes at the University of Waterloo, Canada.</li>

<li><a href="Ali_H._Sayed" title="Ali H. Sayed">Ali H. Sayed</a>, Adaptive Filters, Wiley, NJ, 2008, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-470-25388-5</bdi>.</li>

<li><a href="Thomas_Kailath" title="Thomas Kailath">Thomas Kailath</a>, <a href="Ali_H._Sayed" title="Ali H. Sayed">Ali H. Sayed</a>, and <a href="Babak_Hassibi" title="Babak Hassibi">Babak Hassibi</a>, Linear Estimation, Prentice-Hall, NJ, 2000, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-13-022464-4</bdi>.</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://www.sp4comm.org/">Signal Processing for Communications</a> – free online textbook by Paolo Prandoni and Martin Vetterli (2008)</li>

<li><a rel="nofollow" class="external text" href="http://www.dspguide.com">Scientists and Engineers Guide to Digital Signal Processing</a> – free online textbook by Stephen Smith</li>

<li><a rel="nofollow" class="external text" href="https://www.dsprelated.com/freebooks/sasp/">Julius O. Smith III: Spectral Audio Signal Processing</a> – free online textbook</li>

<li><a rel="nofollow" class="external text" href="https://sites.google.com/view/gsp-website/graph-signal-processing">Graph Signal Processing Website</a> – free online website by Thierry Bouwmans (2025)</li></ul>

/* 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:r1236075235">

/* 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="Digital_signal_processing96" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><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><div id="Digital_signal_processing96" style="font-size:114%;margin:0 4em"><a href="Digital_signal_processing" title="Digital signal processing">Digital signal processing</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theory</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="Detection_theory" title="Detection theory">Detection theory</a></li>

<li><a href="Discrete_time_and_continuous_time" title="Discrete time and continuous time">Discrete signal</a></li>

<li><a href="Estimation_theory" title="Estimation theory">Estimation theory</a></li>

<li><a href="Nyquist%E2%80%93Shannon_sampling_theorem" title="Nyquist–Shannon sampling theorem">Nyquist–Shannon sampling theorem</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Sub-fields</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="Audio_signal_processing" title="Audio signal processing">Audio signal processing</a></li>

<li><a href="Digital_image_processing" title="Digital image processing">Digital image processing</a></li>

<li><a href="Speech_processing" title="Speech processing">Speech processing</a></li>

<li><a href="Statistical_signal_processing" class="mw-redirect" title="Statistical signal processing">Statistical signal processing</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Techniques</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="Z-transform" title="Z-transform">Z-transform</a>

<ul><li><a href="Advanced_z-transform" title="Advanced z-transform">Advanced z-transform</a></li>

<li><a href="Matched_Z-transform_method" title="Matched Z-transform method">Matched Z-transform method</a></li></ul></li>

<li><a href="Bilinear_transform" title="Bilinear transform">Bilinear transform</a></li>

<li><a href="Constant-Q_transform" title="Constant-Q transform">Constant-Q transform</a></li>

<li><a href="Discrete_cosine_transform" title="Discrete cosine transform">Discrete cosine transform</a> (DCT)</li>

<li><a href="Discrete_Fourier_transform" title="Discrete Fourier transform">Discrete Fourier transform</a> (DFT)</li>

<li><a href="Discrete-time_Fourier_transform" title="Discrete-time Fourier transform">Discrete-time Fourier transform</a> (DTFT)</li>

<li><a href="Impulse_invariance" title="Impulse invariance">Impulse invariance</a></li>

<li><a href="Integral_transform" title="Integral transform">Integral transform</a></li>

<li><a href="Laplace_transform" title="Laplace transform">Laplace transform</a></li>

<li><a href="Post's_inversion_formula" class="mw-redirect" title="Post's inversion formula">Post's inversion formula</a></li>

<li><a href="Starred_transform" title="Starred transform">Starred transform</a></li>

<li><a href="Zak_transform" title="Zak transform">Zak transform</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Sampling_(signal_processing)" title="Sampling (signal processing)">Sampling</a></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="Aliasing" title="Aliasing">Aliasing</a></li>

<li><a href="Anti-aliasing_filter" title="Anti-aliasing filter">Anti-aliasing filter</a></li>

<li><a href="Downsampling_(signal_processing)" title="Downsampling (signal processing)">Downsampling</a></li>

<li><a href="Nyquist_rate" title="Nyquist rate">Nyquist rate</a> / <a href="Nyquist_frequency" title="Nyquist frequency">frequency</a></li>

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

<li><a href="Quantization_(signal_processing)" title="Quantization (signal processing)">Quantization</a></li>

<li><a href="Sampling_rate" class="mw-redirect" title="Sampling rate">Sampling rate</a></li>

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

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

</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/Q208163#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata1431" 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/Q208163#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata1431" style="font-size:114%;margin:0 4em">Authority control databases </div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">International</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://id.worldcat.org/fast/1118281">FAST</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">National</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://d-nb.info/gnd/4054947-1">Germany</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh85122397">United States</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb119336198">France</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb119336198">BnF data</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="zpracování signálů"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph135694&CON_LNG=ENG">Czech Republic</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://datos.bne.es/resource/XX539079">Spain</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.nli.org.il/en/authorities/987007543871605171">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-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://www.idref.fr/027253287">IdRef</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://lux.collections.yale.edu/view/concept/801d97e5-94fc-4364-9221-d76fa44ab12c">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 2025-07-24" href="https://en.wikipedia.org/wiki/?title=Signal_processing&oldid=1302202574">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>