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<title>Delta modulation</title>

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

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<p><b>Delta modulation</b> (<b>DM</b>, <b>ΔM</b>, or <b>Δ-modulation</b>) is an <a href="Analog-to-digital_converter" title="Analog-to-digital converter">analog-to-digital</a> and <a href="Digital-to-analog_converter" title="Digital-to-analog converter">digital-to-analog signal</a> conversion technique used for transmission of voice information where quality is not of primary importance. DM is the simplest form of <a href="Differential_pulse-code_modulation" title="Differential pulse-code modulation">differential pulse-code modulation</a> (DPCM) where the difference between successive <a href="Sampling_(signal_processing)" title="Sampling (signal processing)">samples</a> is encoded into n-bit data streams. In delta modulation, the transmitted data are reduced to a 1-bit data stream representing either up (↗) or down (↘). Its main features are:

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<ul><li>The analog signal is approximated with a series of segments.</li>

<li>Each segment of the approximated signal is compared to the preceding bits and the successive bits are determined by this comparison.</li>

<li>Only the change of <a href="Information" title="Information">information</a> is sent, that is, only an increase or decrease of the signal amplitude from the previous sample is sent whereas a no-change condition causes the modulated signal to remain at the same ↗ or ↘ state of the previous sample.</li></ul>

<p>To achieve high <a href="Signal-to-noise_ratio" title="Signal-to-noise ratio">signal-to-noise ratio</a>, delta modulation must use <a href="Oversampling" title="Oversampling">oversampling</a> techniques, that is, the analog signal is sampled at a rate several times higher than the <a href="Nyquist_rate" title="Nyquist rate">Nyquist rate</a>.

</p><p>Derived forms of delta <a href="Modulation" class="mw-redirect" title="Modulation">modulation</a> are <a href="Continuously_variable_slope_delta_modulation" title="Continuously variable slope delta modulation">continuously variable slope delta modulation</a>, <a href="Delta-sigma_modulation" title="Delta-sigma modulation">delta-sigma modulation</a>, and differential modulation. <a href="Differential_pulse-code_modulation" title="Differential pulse-code modulation">Differential pulse-code modulation</a> is the superset of DM.

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

<p>Rather than quantizing the value of the input analog waveform, delta modulation quantizes the difference between the input signal and the integral of all previous quantization steps. This quantized signal effectively represents the <a href="Derivative" title="Derivative">derivative</a> of the input signal,<sup id="cite_ref-:5_1-0" class="reference"><a href="#cite_note-:5-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:2_2-0" class="reference"><a href="#cite_note-:2-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> so the original signal is recovered by integration, as shown in the block diagram in Fig. 2:

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<p>In its simplest form, the quantizer can be realized with a comparator referenced to 0 (a two-level quantizer), whose output is <i>1</i> or <i>-1</i> depending on whether the quantizer's input is positive or negative. The demodulator contains an integrator (just like the one in the feedback loop) whose output rises or falls with each 1 or -1 received. An optional <a href="Low-pass_filter" title="Low-pass filter">low-pass filter</a> will remove high frequency zigzags (see the blue output signal of Fig. 1), so only frequencies in the band of interest remain, to recover a smooth cleaned version of the original signal.

</p><p>Because each sample is only 1 bit, the transmission <a href="Bit_rate" title="Bit rate">bit rate</a> equals the sampling rate.

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<div class="mw-heading mw-heading2"><h2 id="Transfer_characteristics">Transfer characteristics</h2></div>

<p>The two sources of noise in delta modulation are <i>slope overload</i>, when step size is too small to track the original waveform, and <i>granularity</i>, when step size is too large. But a 1971 study shows that slope overload is less objectionable compared to granularity than one might expect based solely on SNR measures.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading3"><h3 id="Slope_overload">Slope overload</h3></div><p>

In delta modulation, there is no limit to the number of pulses of the same sign that may occur, so it is capable of tracking signals of any amplitude without <a href="Clipping_(audio)" title="Clipping (audio)">clipping</a> provided that the signal doesn't change too rapidly.<sup id="cite_ref-:1_5-0" class="reference"><a href="#cite_note-:1-5"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> However, if an input 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 m(t)}">

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

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</math></span><img src="./ea26578dd72bf4dbc3fa391c9feb11eed495699b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.689ex; height:2.843ex;" alt="{\displaystyle m(t)}" loading="lazy"></span> has a <a href="Derivative" title="Derivative">derivative</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 {\dot {m}}(t)}">

<mover>

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

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</math></span><img src="./a71cf25baa3a40181513246bbaee0bb2997b0dd6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.689ex; height:2.843ex;" alt="{\displaystyle {\dot {m}}(t)}" loading="lazy"></span> larger than</p><blockquote><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 |{\dot {m}}(t)|_{max}=\sigma f_{s}}">

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<mover>

</mover>

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</mrow>

</mrow>

</msub>

<msub>

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<annotation encoding="application/x-tex">{\displaystyle |{\dot {m}}(t)|_{max}=\sigma f_{s}}</annotation>

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</math></span><img src="./6b146f74b332b5b6cc6e00902e1c0ae856615300.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:16.039ex; height:3.009ex;" alt="{\displaystyle |{\dot {m}}(t)|_{max}=\sigma f_{s}}" loading="lazy"></span>,</p></blockquote><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_{s}}">

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</mrow>

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

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</math></span><img src="./34f933ad7a8dc310b3fa8e9f7b0b2558cba136db.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.143ex; height:2.509ex;" alt="{\displaystyle f_{s}}" loading="lazy"></span> is the sampling frequency 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 \sigma }">

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

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</math></span><img src="./59f59b7c3e6fdb1d0365a494b81fb9a696138c36.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle \sigma }" loading="lazy"></span> is the quantization step size, then the signal changes too fast, causing slope overload. For example, if the input signal is a cosine wave with 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 \omega }">

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

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</math></span><img src="./48eff443f9de7a985bb94ca3bde20813ea737be8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.446ex; height:1.676ex;" alt="{\displaystyle \omega }" loading="lazy"></span> and 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}">

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

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</math></span><img src="./7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"></span>,

</p><dl><dd><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 m(t)={A\cos(\omega t)}}">

</mrow>

</mstyle>

</mrow>

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

</semantics>

</math></span><img src="./eb55c305fba923e95abf6400128906bb9a46fc15.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.124ex; height:2.843ex;" alt="{\displaystyle m(t)={A\cos(\omega t)}}" loading="lazy"></span>,</dd></dl>

<p>then its derivative,

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<mover>

</mover>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\dot {m}}(t)=-\omega A\sin(\omega t)}</annotation>

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</math></span><img src="./2c478518d9f67a2cf57c770084327673ab9ed664.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.122ex; height:2.843ex;" alt="{\displaystyle {\dot {m}}(t)=-\omega A\sin(\omega t)}" loading="lazy"></span>,</dd></dl>

<p>can be as large as

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</mrow>

<mover>

</mover>

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<annotation encoding="application/x-tex">{\displaystyle |{\dot {m}}(t)|_{max}=\omega A}</annotation>

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</math></span><img src="./8b92662b1ae48611cbfb6c47942048c8c5689da5.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:15.755ex; height:3.009ex;" alt="{\displaystyle |{\dot {m}}(t)|_{max}=\omega A}" loading="lazy"></span>.</dd></dl>

<p>Thus, slope overload won't occur for a sinusoidal input if

</p>

<msub>

</mrow>

</msub>

</mstyle>

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<annotation encoding="application/x-tex">{\displaystyle \omega A<\sigma f_{s}}</annotation>

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</math></span><img src="./6f28f4c0099cd04247d33ada50a8d8c3a59fb227.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.76ex; height:2.509ex;" alt="{\displaystyle \omega A<\sigma f_{s}}" loading="lazy"></span>.</dd></dl>

<p>Consequently, a sinusoidal signal can be transmitted without slope overload if its amplitude is not bigger than

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<msub>

</mrow>

</msub>

<mfrac>

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<msub>

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<annotation encoding="application/x-tex">{\displaystyle A_{max}={\sigma f_{s} \over \omega }}</annotation>

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</math></span><img src="./e271e8268245a2a657d72c8d305ba50c961f3754.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.635ex; height:5.343ex;" alt="{\displaystyle A_{max}={\sigma f_{s} \over \omega }}" loading="lazy"></span>.</dd></dl>

<p>A real input signal may be more complex than a single sinusoid, but this example illustrates how a transmitted signal may be attenuated depending on the sampling frequency, step size, and the input signal's frequency.

</p><p>While slope overload (also referred to as slope clipping) can be avoided by increasing the quantum step size or sampling rate, very high sampling rates, typically 20 times the highest frequency of interest, are required to achieve the same quality as <a href="Pulse-code_modulation" title="Pulse-code modulation">pulse-code modulation</a> (PCM).<sup id="cite_ref-:1_5-1" class="reference"><a href="#cite_note-:1-5"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading3"><h3 id="Inability_to_transmit_DC">Inability to transmit DC</h3></div>

<p>Because the modulated signal contains only the derivative of the input, any <a href="DC_bias" title="DC bias">DC</a> and low-frequency content of the signal is lost (which may be ok for voice and other applications which do not have low frequencies), transmission errors are accumulated, and high-frequency noise is amplified. An improvement to DM called <a href="Delta-sigma_modulation" title="Delta-sigma modulation">delta-sigma modulation</a> avoids these downsides by rearranging the integrator's position so that the modulated signal represents the amplitude of the input signal instead of just its derivative.<sup id="cite_ref-:5_1-1" class="reference"><a href="#cite_note-:5-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:2_2-1" class="reference"><a href="#cite_note-:2-2"><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>The seminal<sup id="cite_ref-:0_6-0" class="reference"><a href="#cite_note-:0-6"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> paper combining feedback with oversampling to achieve delta modulation was by F. de Jager of <a href="Philips_Research_Laboratories" class="mw-redirect" title="Philips Research Laboratories">Philips Research Laboratories</a> in 1952.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Initial patents include:

</p>

<ul><li>"Communication system utilizing constant amplitude pulses of opposite polarities" by <a href="Maurice_Deloraine" title="Maurice Deloraine">Maurice Deloraine</a> et. al. (French patent issued 1946, US patent filed 1947).<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup></li>

<li>"Differential quantization of communication signals" by <a href="C._Chapin_Cutler" title="C. Chapin Cutler">C. Chapin Cutler</a> (filed 1950),<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> which describes <a href="Differential_PCM" class="mw-redirect" title="Differential PCM">differential PCM</a> and delta modulation (1-bit DPCM).</li></ul>

<div class="mw-heading mw-heading2"><h2 id="Asynchronous_delta_modulation">Asynchronous delta modulation</h2></div>

<p>The 1947 Deloraine, 1950 Cutler, and 1952 Jager designs were <a href="Synchronous_circuit" title="Synchronous circuit">synchronous</a> (or time-quantized). Delta modulation is also possible without a fixed sampling rate. A February 1966 paper by H. Inose "Asynchronous delta-modulation system"<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> uses <a href="Schmitt_trigger" title="Schmitt trigger">Schmitt triggers</a> to detect when the input signal exceeds the local demodulator by a predetermined difference, with the benefit of reducing the number of output pulses. A November 1973 paper "Signal Coding Using Asynchronous Delta Modulation" (presented in 1974)<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> investigates an algorithm that varies the sampling rate to transmit fewer samples during periods of small signal variation.

</p>

<div class="mw-heading mw-heading2"><h2 id="Adaptive_delta_modulation">Adaptive delta modulation</h2></div>

<p>Adaptive delta modulation (ADM) was first published by Dr. John E. Abate (<a href="Bell_Labs" title="Bell Labs">Bell Labs</a> Fellow) in his doctoral thesis at <a href="New_Jersey_Institute_of_Technology" title="New Jersey Institute of Technology">NJ Institute Of Technology</a> in 1968.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> ADM was later selected as the standard for all <a href="NASA" title="NASA">NASA</a> communications between mission control and space-craft.

</p><p>In the mid-1980s, Massachusetts audio company <a href="Dbx_(company)" title="Dbx (company)">DBX</a> marketed a commercially unsuccessful digital recording system based on adaptive delta modulation. See <a href="Dbx_Model_700_Digital_Audio_Processor" title="Dbx Model 700 Digital Audio Processor">DBX 700</a>.

</p><p>Adaptive delta modulation or <a href="Continuously_variable_slope_delta_modulation" title="Continuously variable slope delta modulation">Continuously variable slope delta modulation</a> (CVSD) is a modification of DM in which the step size is not fixed. Rather, when several consecutive bits have the same direction value, the encoder and decoder assume that slope overload is occurring, and the step size becomes progressively larger.

</p><p>Otherwise, the step size becomes gradually smaller over time. ADM reduces slope error, at the expense of increasing <a href="Quantization_error" class="mw-redirect" title="Quantization error">quantization error</a>. This error can be reduced by using a low-pass filter. ADM provides robust performance in the presence of bit errors meaning error detection and correction are not typically used in an ADM radio design, it is this very useful technique that allows for adaptive-delta-modulation.

</p>

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

<div class="mw-heading mw-heading3"><h3 id="Video_game_sound_effects">Video game sound effects</h3></div>

<p>The <a href="Nintendo_Entertainment_System" title="Nintendo Entertainment System">Nintendo Entertainment System</a>'s audio processing unit (the <a href="Ricoh_2A03" title="Ricoh 2A03">Ricoh 2A03</a> chip) includes a Delta Modulation Channel (DMC) to demodulate percussion and sound effects. The DMC reads delta-encoded audio data via <a href="Direct_memory_access" title="Direct memory access">direct memory access</a> into a <a href="Shift_register" title="Shift register">shift register</a>, which gets shifted out <a href="Serial_communication" title="Serial communication">serially</a> into an <a href="Up/down_counter" class="mw-redirect" title="Up/down counter">up/down counter</a> acting as the demodulator's integrator. Because the shift register is clocked by a configurable timer, the audio's frequency can be shifted by adjusting the playback speed. The counter's value is outputted though a 7-bit <a href="Digital-to-analog_converter" title="Digital-to-analog converter">digital-to-analog converter</a> (DAC). Note: writing PCM samples directly to the counter bypasses the DM demodulation to instead provide low-bit PCM output.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading3"><h3 id="Satellite_Business_Systems_24_kbps_delta_modulation">Satellite Business Systems 24 kbps delta modulation</h3></div>

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<p>Delta modulation was used by <a href="Satellite_Business_Systems" title="Satellite Business Systems">Satellite Business Systems</a> (SBS) for its voice ports to provide long distance phone service to large domestic corporations with a significant inter-corporation communications need (such as <a href="IBM" title="IBM">IBM</a>). Each traffic channel had a 32 kbit/s bitrate.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> This system was in service throughout the 1980s. The voice ports used <b>digitally implemented 24 kbit/s delta modulation</b> with Voice Activity Compression (VAC) and <a href="Echo_suppressor" class="mw-redirect" title="Echo suppressor">echo suppressors</a> to control the half second echo path through the satellite. They performed formal listening tests to verify the <b>24 kbit/s delta modulator</b> achieved <b>full voice quality</b> with no discernible degradation as compared to a high quality phone line or the standard 64 kbit/s <a href="%CE%9C-law" class="mw-redirect" title="Μ-law">μ-law</a> <a href="Companding" title="Companding">companded</a> PCM. This provided an eight to three improvement in satellite channel capacity. IBM developed the Satellite Communications Controller and the voice port functions.

</p><p>The original proposal in 1974, used a state-of-the-art 24 kbit/s delta modulator with a single integrator and a <i>Shindler Compander</i> modified for gain error recovery. This proved to have less than full phone line speech quality. In 1977, one engineer with two assistants in the IBM <a href="Research_Triangle_Park" title="Research Triangle Park">Research Triangle Park</a>, NC laboratory was assigned to improve the quality.

</p><p>The final implementation replaced the integrator with a <b>predictor</b> implemented with a two pole complex pair low-pass filter designed to approximate the long term average speech spectrum. The theory was that ideally the integrator should be a predictor designed to match the signal spectrum. A nearly perfect Shindler Compander replaced the modified version. It was found the modified compander resulted in a less than perfect step size at most signal levels and the fast gain error recovery increased the noise as determined by actual listening tests as compared to simple signal to noise measurements. The final compander achieved a very mild gain error recovery due to the natural truncation <a href="Rounding_error" class="mw-redirect" title="Rounding error">rounding error</a> caused by twelve bit arithmetic.

</p><p>The complete function of delta modulation, VAC and Echo Control for six ports was implemented in a single digital integrated circuit chip with twelve bit arithmetic. A single <a href="Digital-to-analog_converter" title="Digital-to-analog converter">digital-to-analog converter</a> (DAC) was shared by all six ports providing voltage compare functions for the modulators and feeding sample and hold circuits for the demodulator outputs. A single card held the chip, DAC and all the analog circuits for the phone line interface including transformers.

</p>

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

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<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">The quantizer is synchronized to some sort of clock in synchronous versions. The original 1947 Deloraine and 1950 Cutler patents and the 1952 Jager paper used some pulse generator to control the quantizer so that the samples were time-quantized. The above asynchronous modulator circuit won't work with ideal elements which have no delay, because the loop would happen instantaneously. But real circuits will unavoidably have some amount of delay or hysteresis, which the above asynchronous modulator circuit would require.</span>

</li>

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

<ul><li><a href="Adaptive_differential_pulse-code_modulation" title="Adaptive differential pulse-code modulation">Adaptive differential pulse-code modulation</a></li>

<li><a href="Analog-to-digital_converter" title="Analog-to-digital converter">Analog-to-digital converter</a> (ADC)</li>

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

<li><a href="Pulse-code_modulation" title="Pulse-code modulation">Pulse-code modulation</a></li>

<li><a href="Pulse-density_modulation" title="Pulse-density modulation">Pulse-density modulation</a>

<ul><li><a href="Delta-sigma_modulation" title="Delta-sigma modulation">Delta-sigma modulation</a></li>

<li><a href="Direct_Stream_Digital" title="Direct Stream Digital">Direct Stream Digital</a></li></ul></li></ul>

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

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</style><cite id="CITEREFSteele1975" class="citation book cs1">Steele, R. (1975). <i>Delta Modulation Systems</i>. London: Pentech Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-470-82104-3</bdi>.</cite></li>

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</style><span class="citation FS1037C MS188"><span class="noviewer" typeof="mw:File"><span></span></span> This article incorporates <a href="Copyright_status_of_works_by_the_federal_government_of_the_United_States" title="Copyright status of works by the federal government of the United States">public domain material</a> from <cite class="citation cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20220122224547/https://www.its.bldrdoc.gov/fs-1037/fs-1037c.htm"><i>Federal Standard 1037C</i></a>. <a href="General_Services_Administration" title="General Services Administration">General Services Administration</a>. Archived from <a rel="nofollow" class="external text" href="https://www.its.bldrdoc.gov/fs-1037/fs-1037c.htm">the original</a> on 2022-01-22.</cite> (in support of <a href="MIL-STD-188" title="MIL-STD-188">MIL-STD-188</a>).</span></li></ul>

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<li id="cite_note-:1-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-:1_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:1_5-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><cite id="CITEREFKester2008" class="citation web cs1">Kester, Walt (2008). <a rel="nofollow" class="external text" href="https://www.analog.com/media/en/training-seminars/tutorials/MT-022.pdf">"ADC Architectures II: Sigma-Delta ADC Basics"</a> <span class="cs1-format">(PDF)</span>. <i><a href="Analog_Devices" title="Analog Devices">Analog Devices</a></i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230818131208/https://www.analog.com/media/en/training-seminars/tutorials/MT-022.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 2023-08-18<span class="reference-accessdate">. Retrieved <span class="nowrap">2023-08-20</span></span>.</cite></span>

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<li id="cite_note-:0-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-:0_6-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFWooley2012" class="citation web cs1">Wooley, Bruce A. (2012-03-22). <a rel="nofollow" class="external text" href="https://r6.ieee.org/scv-sscs/wp-content/uploads/sites/80/2012/06/Oversampling-Wooley_SCV-ver2.pdf">"The Evolution of Oversampling Analog-to-Digital Converters"</a> <span class="cs1-format">(PDF)</span>. <i><a href="IEEE" class="mw-redirect" title="IEEE">IEEE</a></i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230628235029/https://r6.ieee.org/scv-sscs/wp-content/uploads/sites/80/2012/06/Oversampling-Wooley_SCV-ver2.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 2023-06-28<span class="reference-accessdate">. Retrieved <span class="nowrap">2023-06-28</span></span>.</cite></span>

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

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

<ul><li><a rel="nofollow" class="external text" href="http://www.owlnet.rice.edu/~elec301/Projects99/adda/dmod.html">Delta Modulator</a></li></ul>

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</style><div id="Data_compression_methods241" style="font-size:114%;margin:0 4em"><a href="Data_compression" title="Data compression">Data compression</a> methods</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Lossless_compression" title="Lossless compression">Lossless</a><br>type</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="Entropy_coding" title="Entropy coding">Entropy</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="Adaptive_coding" title="Adaptive coding">Adaptive coding</a></li>

<li><a href="Arithmetic_coding" title="Arithmetic coding">Arithmetic</a></li>

<li><a href="Asymmetric_numeral_systems" title="Asymmetric numeral systems">Asymmetric numeral systems</a></li>

<li><a href="Golomb_coding" title="Golomb coding">Golomb</a></li>

<li><a href="Huffman_coding" title="Huffman coding">Huffman</a>

<ul><li><a href="Adaptive_Huffman_coding" title="Adaptive Huffman coding">Adaptive</a></li>

<li><a href="Canonical_Huffman_code" title="Canonical Huffman code">Canonical</a></li>

<li><a href="Modified_Huffman_coding" title="Modified Huffman coding">Modified</a></li></ul></li>

<li><a href="Range_coding" title="Range coding">Range</a></li>

<li><a href="Shannon_coding" title="Shannon coding">Shannon</a></li>

<li><a href="Shannon%E2%80%93Fano_coding" title="Shannon–Fano coding">Shannon–Fano</a></li>

<li><a href="Shannon%E2%80%93Fano%E2%80%93Elias_coding" title="Shannon–Fano–Elias coding">Shannon–Fano–Elias</a></li>

<li><a href="Tunstall_coding" title="Tunstall coding">Tunstall</a></li>

<li><a href="Unary_coding" title="Unary coding">Unary</a></li>

<li><a href="Universal_code_(data_compression)" title="Universal code (data compression)">Universal</a>

<ul><li><a href="Exponential-Golomb_coding" title="Exponential-Golomb coding">Exp-Golomb</a></li>

<li><a href="Fibonacci_coding" title="Fibonacci coding">Fibonacci</a></li>

<li><a href="Elias_gamma_coding" title="Elias gamma coding">Gamma</a></li>

<li><a href="Levenshtein_coding" title="Levenshtein coding">Levenshtein</a></li></ul></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Dictionary_coder" title="Dictionary coder">Dictionary</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="Byte-pair_encoding" title="Byte-pair encoding">Byte-pair encoding</a></li>

<li><a href="LZ77_and_LZ78" title="LZ77 and LZ78">Lempel–Ziv</a>

<li><a href="Snappy_(compression)" title="Snappy (compression)">Snappy</a></li></ul></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">

<li><a href="Delta_encoding" title="Delta encoding">Delta</a>

<ul><li><a href="Incremental_encoding" title="Incremental encoding">Incremental</a></li></ul></li>

<li><a href="Grammar-based_code" title="Grammar-based code">Grammar</a>

<li><a href="Sequitur_algorithm" title="Sequitur algorithm">Sequitur</a></li></ul></li>

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

<ul><li>LZ77 + Huffman

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

<li>LZ77 + ANS

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

<li>LZ77 + Huffman + ANS

<ul><li><a href="Zstd" title="Zstd">Zstandard</a></li></ul></li>

<li>LZ77 + Huffman + context

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

<li>LZSS + Huffman

<li>LZ77 + Range

<li>LZHAM</li></ul></li>

<li>RLE + BWT + MTF + Huffman

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Lossy_compression" title="Lossy compression">Lossy</a><br>type</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="Transform_coding" title="Transform coding">Transform</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="Discrete_cosine_transform" title="Discrete cosine transform">Discrete cosine transform</a>

<li><a href="Wavelet_transform" title="Wavelet transform">Wavelet</a>

<ul><li><a href="Daubechies_wavelet" title="Daubechies wavelet">Daubechies</a></li>

<li><a href="Set_partitioning_in_hierarchical_trees" title="Set partitioning in hierarchical trees">SPIHT</a></li></ul></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Predictive</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="Adaptive_differential_pulse-code_modulation" title="Adaptive differential pulse-code modulation">ADPCM</a></li></ul></li>

<ul><li><a href="Algebraic_code-excited_linear_prediction" title="Algebraic code-excited linear prediction">ACELP</a></li>

<li>Motion

<ul><li><a href="Motion_compensation" title="Motion compensation">Compensation</a></li>

<li><a href="Motion_estimation" title="Motion estimation">Estimation</a></li>

<li><a href="Motion_vector" class="mw-redirect" title="Motion vector">Vector</a></li></ul></li>

<li><a href="Psychoacoustics" title="Psychoacoustics">Psychoacoustic</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Data_compression#Audio" title="Data compression">Audio</a></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%">Concepts</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="Companding" title="Companding">Companding</a></li>

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

<li><a href="Dynamic_range" title="Dynamic range">Dynamic range</a></li>

<li><a href="Latency_(audio)" title="Latency (audio)">Latency</a></li>

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

<li><a href="Sampling_(signal_processing)" title="Sampling (signal processing)">Sampling</a></li>

<li><a href="Silence_compression" title="Silence compression">Silence compression</a></li>

<li><a href="Sound_quality" title="Sound quality">Sound quality</a></li>

<li><a href="Speech_coding" title="Speech coding">Speech coding</a></li>

<li><a href="Sub-band_coding" title="Sub-band coding">Sub-band coding</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Audio_codec" title="Audio codec">Codec</a><br>parts</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="Adaptive_differential_pulse-code_modulation" title="Adaptive differential pulse-code modulation">ADPCM</a></li>

</ul></li>

<ul><li><a href="Algebraic_code-excited_linear_prediction" title="Algebraic code-excited linear prediction">ACELP</a></li>

<li><a href="Psychoacoustics" title="Psychoacoustics">Psychoacoustic model</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Image_compression" title="Image compression">Image</a></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%">Concepts</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="Chroma_subsampling" title="Chroma subsampling">Chroma subsampling</a></li>

<li><a href="Coding_tree_unit" title="Coding tree unit">Coding tree unit</a></li>

<li><a href="Color_space" title="Color space">Color space</a></li>

<li><a href="Compression_artifact" title="Compression artifact">Compression artifact</a></li>

<li><a href="Image_resolution" title="Image resolution">Image resolution</a></li>

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

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

<li><a href="Quantization_(image_processing)" title="Quantization (image processing)">Quantization</a></li>

<li><a href="Standard_test_image" title="Standard test image">Standard test image</a></li>

<li><a href="Texture_compression" title="Texture compression">Texture compression</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Methods</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="Chain_code" title="Chain code">Chain code</a></li>

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

<li><a href="Fractal_compression" title="Fractal compression">Fractal</a></li>

<li><a href="Wavelet_transform" title="Wavelet transform">Wavelet</a>

<ul><li><a href="Daubechies_wavelet" title="Daubechies wavelet">Daubechies</a></li>

<li><a href="Set_partitioning_in_hierarchical_trees" title="Set partitioning in hierarchical trees">SPIHT</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="Data_compression#Video" title="Data compression">Video</a></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%">Concepts</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="Display_resolution" title="Display resolution">Display resolution</a></li>

<li><a href="Film_frame" title="Film frame">Frame</a></li>

<li><a href="Frame_rate" title="Frame rate">Frame rate</a></li>

<li><a href="Video_compression_picture_types" title="Video compression picture types">Frame types</a></li>

<li><a href="Interlaced_video" title="Interlaced video">Interlace</a></li>

<li><a href="Video#Characteristics_of_video_streams" title="Video">Video characteristics</a></li>

<li><a href="Video_quality" title="Video quality">Video quality</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Video_codec" title="Video codec">Codec</a><br>parts</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="Deblocking_filter" title="Deblocking filter">Deblocking filter</a></li>

<li><a href="Lapped_transform" title="Lapped transform">Lapped transform</a></li>

<li>Motion

<ul><li><a href="Motion_compensation" title="Motion compensation">Compensation</a></li>

<li><a href="Motion_estimation" title="Motion estimation">Estimation</a></li>

<li><a href="Motion_vector" class="mw-redirect" title="Motion vector">Vector</a></li></ul></li>

<li><a href="Wavelet_transform" title="Wavelet transform">Wavelet</a>

<ul><li><a href="Daubechies_wavelet" title="Daubechies wavelet">Daubechies</a></li>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Information_theory" title="Information theory">Theory</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="Compressed_data_structure" title="Compressed data structure">Compressed data structures</a>

<ul><li><a href="Compressed_suffix_array" title="Compressed suffix array">Compressed suffix array</a></li>

<li><a href="FM-index" title="FM-index">FM-index</a></li></ul></li>

<li><a href="Entropy_(information_theory)" title="Entropy (information theory)">Entropy</a></li>

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

<ul><li><a href="Timeline_of_information_theory" title="Timeline of information theory">Timeline</a></li></ul></li>

<li><a href="Kolmogorov_complexity" title="Kolmogorov complexity">Kolmogorov complexity</a></li>

<li><a href="Prefix_code" title="Prefix code">Prefix code</a></li>

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

<li><a href="Rate%E2%80%93distortion_theory" title="Rate–distortion theory">Rate–distortion</a></li>

<li><a href="Redundancy_(information_theory)" title="Redundancy (information theory)">Redundancy</a></li>

<li><a href="Data_compression_symmetry" title="Data compression symmetry">Symmetry</a></li>

<li><a href="Smallest_grammar_problem" title="Smallest grammar problem">Smallest grammar problem</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Community</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="Hutter_Prize" title="Hutter Prize">Hutter Prize</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">People</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="Mark_Adler" title="Mark Adler">Mark Adler</a></li>

</div></td></tr></tbody></table></div></div><div><div class="zim-footer">

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