{ "id": "epnc9q8dj4", "slug": "delta-modulation", "title": "Delta modulation", "updated": "2026-10-21", "topic_path": [ { "id": "technology", "label": "Technology and the built world", "api_url": "https://www.edgepedia.org/api/v1/topics/technology" }, { "id": "technology.computing", "label": "Computing and digital systems", "api_url": "https://www.edgepedia.org/api/v1/topics/technology.computing" }, { "id": "technology.computing.ai", "label": "Artificial intelligence and data", "api_url": "https://www.edgepedia.org/api/v1/topics/technology.computing.ai" }, { "id": "technology.computing.ai.algorithms", "label": "Algorithms and computational methods", "api_url": "https://www.edgepedia.org/api/v1/topics/technology.computing.ai.algorithms" }, { "id": "technology.computing.ai.numerical_string_geometry", "label": "Numerical, string, and geometric algorithms", "api_url": "https://www.edgepedia.org/api/v1/topics/technology.computing.ai.numerical_string_geometry" }, { "id": "technology.computing.ai.numerical_string_geometry.fourier_signal_transforms", "label": "Fourier and signal transforms", "api_url": "https://www.edgepedia.org/api/v1/topics/technology.computing.ai.numerical_string_geometry.fourier_signal_transforms" } ], "geo": [ { "id": "geo.nongeo.t1946.technology.computing.ai.numerical_string_geometry.fourier_signal_transforms", "label": "Non-geographic · 1946 to 2000: Fourier and signal transforms", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.technology.computing.ai.numerical_string_geometry.fourier_signal_transforms", "path": [ { "id": "geo.nongeo", "label": "Non-geographic", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo" }, { "id": "geo.nongeo.t1946", "label": "Non-geographic · 1946 to 2000", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946" }, { "id": "geo.nongeo.t1946.technology", "label": "Technology and the built world", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.technology" }, { "id": "geo.nongeo.t1946.technology.computing", "label": "Computing and digital systems", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.technology.computing" }, { "id": "geo.nongeo.t1946.technology.computing.ai", "label": "Artificial intelligence and data", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.technology.computing.ai" }, { "id": "geo.nongeo.t1946.technology.computing.ai.algorithms", "label": "Algorithms and computational methods", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.technology.computing.ai.algorithms" }, { "id": "geo.nongeo.t1946.technology.computing.ai.numerical_string_geometry", "label": "Numerical, string, and geometric algorithms", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.technology.computing.ai.numerical_string_geometry" }, { "id": "geo.nongeo.t1946.technology.computing.ai.numerical_string_geometry.fourier_signal_transforms", "label": "Fourier and signal transforms", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.technology.computing.ai.numerical_string_geometry.fourier_signal_transforms" } ] } ], "excerpt": "Delta modulation is an analog-to-digital encoding method that represents a waveform with one bit per sample, sending whether the signal rose or fell; it underlies sigma-delta converters.", "snippet": "Delta modulation is an analog-to-digital encoding method that represents a waveform with one bit per sample, sending whether the signal rose or fell; it underlies sigma-delta converters.", "node": "technology.computing.ai.numerical_string_geometry.fourier_signal_transforms", "markdown": "# Delta modulation\n\nDelta modulation (DM) is an analog-to-digital encoding method that represents a waveform by the sign of its difference from an accumulated approximation, transmitting one bit per sampling instant. It is a minimal form of differential pulse code modulation (DPCM): instead of coding each sample's amplitude with an n-bit word, the encoder sends only whether the signal rose or fell since the last step.[1](https://ntrs.nasa.gov/api/citations/19700001976/downloads/19700001976.pdf) • [2](https://www.eng.auburn.edu/~troppel/courses/TIMS-manuals-r5/TIMS%20Experiment%20Manuals/Student_Text/Vol-D1/D1-13.pdf) The scheme was devised as a simplified form of PCM that avoided the then-difficult multibit analog-to-digital converter, and it remains the conceptual basis of sigma-delta converters and of event-based signal encoders.[2](https://www.eng.auburn.edu/~troppel/courses/TIMS-manuals-r5/TIMS%20Experiment%20Manuals/Student_Text/Vol-D1/D1-13.pdf)\n\n| Key fact | Value |\n|---|---|\n| Bits per sample | 1 (two-level quantizer); sample rate equals bit rate[3](https://www.raffia.ch/content/datasheets/volume01/Tutorial_DeltaMod_CVSD_MxCom.pdf) |\n| Typical oversampling for voice | 8 to 16 times the Nyquist rate[4](https://technav.ieee.org/topic/delta-modulation/) |\n| Bit rate for 4 kHz speech | About 100 kbit/s or more[2](https://www.eng.auburn.edu/~troppel/courses/TIMS-manuals-r5/TIMS%20Experiment%20Manuals/Student_Text/Vol-D1/D1-13.pdf) |\n| Clock for 1 kHz voice input | Minimum 9600 Hz, ideally 64 kHz[5](https://www.raffia.ch/content/datasheets/volume01/AN1544_DeltaMod_CVSD_Motorola.pdf) |\n| Bandwidth vs PCM | 2:1 to 3:1 reduction with simple hardware[1](https://ntrs.nasa.gov/api/citations/19700001976/downloads/19700001976.pdf) |\n| Maximum slope trackable | Step size k divided by sampling interval T[1](https://ntrs.nasa.gov/api/citations/19700001976/downloads/19700001976.pdf) |\n| Best-known adaptive variant | CVSD, standardized in MIL-STD-188-113 and Fed-Std-1023[6](https://www.mathworks.com/help/dsp/ug/comparison-of-ldm-cvsd-and-adpcm.html) |\n\n## How it works\n\nThe encoder compares the input signal against its own integrated output and transmits the sign of the error. With input \\( m(nT_{s}) \\) and staircase approximation \\( m_{q} \\), the error, quantized error, and accumulator update are[7](https://uomus.edu.iq/img/lectures21/MUCLecture_2023_6446207.pdf)\n\n\\[ e(nT_{s}) = m(nT_{s}) - m_{q}(nT_{s} - T_{s}) \\]\n\\[ e_{q}(nT_{s}) = \\Delta \\cdot \\mathrm{Sgn}[e(nT_{s})] \\]\n\\[ m_{q}(nT_{s}) = m_{q}(nT_{s} - T_{s}) + e_{q}(nT_{s}) \\]\n\nso the accumulator increments the approximation by a step \\( \\Delta \\) upward or downward according to the sign of the error. In the equivalent continuous-time description, a one-bit quantizer outputs +k when the error between input x(t) and the integrated feedback y(t) is positive and −k when it is negative, with sampling interval T and sampling frequency \\( f = 1/T \\).[1](https://ntrs.nasa.gov/api/citations/19700001976/downloads/19700001976.pdf) Because only one bit is conveyed per sample, the signal must be oversampled heavily; eight to sixteen times the [Nyquist rate](https://www.edgepedia.org/nyquist-rate) is typical for voice-bandwidth signals, and higher clock rates give better modulation quality.[4](https://technav.ieee.org/topic/delta-modulation/) • [5](https://www.raffia.ch/content/datasheets/volume01/AN1544_DeltaMod_CVSD_Motorola.pdf)\n\nQuantization error is conventionally split into two components. Granular noise arises because the integrator output is constrained to integral multiples of the step size k, so it oscillates around a slowly changing input. Slope overload noise arises when the input's slope exceeds the maximum the modulator can follow, \\( k/T \\).[1](https://ntrs.nasa.gov/api/citations/19700001976/downloads/19700001976.pdf) Minimizing one distortion works against the other: slope overload calls for a larger step, granular noise for a smaller one, so the optimum step size for minimum mean-square error is a compromise.[7](https://uomus.edu.iq/img/lectures21/MUCLecture_2023_6446207.pdf)\n\n## How it is done\n\nA practical delta modulator is a simple control loop with a comparator in the forward path and an integrator in the feedback path.[5](https://www.raffia.ch/content/datasheets/volume01/AN1544_DeltaMod_CVSD_Motorola.pdf) The steps at the encoder are:\n\n1. Periodically sample the input message (a clock sets the sampling instants).\n2. Compare the current sample with the accumulated feedback value in a comparator; the comparator measures the sign of the difference between the input analog signal and the integrator output.\n3. Emit one bit: a logic 1 steps the integrator up, a logic 0 steps it down.[4](https://technav.ieee.org/topic/delta-modulation/)\n\nThe demodulator is simply a staircase generator, incrementing positively on a one and negatively on a zero, usually followed by a lowpass smoothing filter.[8](http://dip.ee.uct.ac.za/~nicolls/lectures/eee482f/07_dpcm.pdf)\n\n## Origin\n\nA 1970 NASA technical report traces the first appearance of delta modulation in the Western literature to a French patent, with the first English-language occurrences in de Jager's 1952 Philips Research Report paper and a 1952 paper by Schouten, de Jager, and Greefkes.[1](https://ntrs.nasa.gov/api/citations/19700001976/downloads/19700001976.pdf) An Analog Devices tutorial names ITT Laboratories in France as the origin, and notes the principle was rediscovered several times afterwards.[9](https://www.analog.com/media/en/training-seminars/tutorials/MT-022.pdf?doc=AN-1521.pdf)\n\n## Variants\n\n**Linear DM and DPCM.** Plain (linear) DM is a very simple DPCM system with a 1-bit, two-level quantizer that can represent only sample-to-sample differences of \\( \\Delta \\); distortion grows when the actual difference differs greatly from \\( \\Delta \\), and the remedy is to sample at a very high rate.[10](https://www.ece.mcmaster.ca/~shirani/multi12/differential.pdf)\n\n**Adaptive DM and CVSD.** Continuously variable slope delta (CVSD) modulation is linear DM with an adaptive step size: a slope-overload detector and syllabic filter drive a pulse amplitude modulator that increases the step size when the input slope changes too quickly and decreases it when the slope changes slowly.[6](https://www.mathworks.com/help/dsp/ug/comparison-of-ldm-cvsd-and-adpcm.html) Equivalently, the step grows after several consecutive identical bits and shrinks when bits alternate.[4](https://technav.ieee.org/topic/delta-modulation/)\n\n**Sigma-delta modulation.** The single-bit oversampling noise-shaping architecture was elaborated on, implementing first- and second-order sigma-delta modulators with solid-state circuits.[11](https://www.iosrjournals.org/iosr-jece/papers/Vol.%2011%20Issue%203/Version-2/M1103028794.pdf) A sigma-delta modulator oversamples above the Nyquist rate and uses a feedback loop with a 1-bit quantizer and DAC to push quantization noise to higher frequencies, where it is filtered out.[12](https://www.nature.com/articles/s41598-025-19272-4)\n\n## Applications\n\nDelta modulation was attractive for voice communications in the 1960s and 1970s because its reduced circuit complexity outweighed a modest signal-quality loss compared with PCM.[4](https://technav.ieee.org/topic/delta-modulation/) CVSD became an accepted standard in the tactical community, used for decades in military voice encryption per MIL-STD-188-113 (16 kbit/s and 32 kbit/s) and Federal Standard 1023 (12 kbit/s), and it persists in [Bluetooth](https://www.edgepedia.org/bluetooth) audio codecs at low bit rates and in point-to-point wireless products such as digital cordless telephones and digital Land Mobile Radio.[6](https://www.mathworks.com/help/dsp/ug/comparison-of-ldm-cvsd-and-adpcm.html) • [4](https://technav.ieee.org/topic/delta-modulation/) • [3](https://www.raffia.ch/content/datasheets/volume01/Tutorial_DeltaMod_CVSD_MxCom.pdf)\n\n**Event-based sensing.** The same principle now appears in neuromorphic front-ends. The basic Asynchronous Delta Modulator circuit belongs to the class of level-crossing ADCs in which the sampling interval adapts to the signal, a concept traced to Inose and colleagues in 1966; it uses two comparators with up- and down-delta thresholds and tags output events UP or DN by the polarity of the level crossing.[13](https://arxiv.org/html/2607.12901)\n\n## Limitations and alternatives\n\nThe central limitation is the step-size compromise. A linear delta modulator exhibits slope overload while the signal changes rapidly and granular noise while the signal is constant; CVSD and ADPCM mitigate both with a variable step size, and ADPCM gives more accuracy at the cost of extra computation.[6](https://www.mathworks.com/help/dsp/ug/comparison-of-ldm-cvsd-and-adpcm.html) Relative to PCM, delta modulation admits simpler analog-to-digital and digital-to-analog conversion, but its sampling rate is higher than PCM's and in many cases the transmission rate is also higher.[14](https://www.worldradiohistory.com/Archive-Bell-System-Technical-Journal/60s/Bell-System-Technical-Journal-1969-2-Complete.pdf) Its advantage is a 2:1 to 3:1 bandwidth reduction relative to PCM with simple implementation, while techniques achieving larger compression require significantly more sophisticated hardware.[1](https://ntrs.nasa.gov/api/citations/19700001976/downloads/19700001976.pdf)\n\nThe achievable quality is bounded by the oversampling ratio. Using Abate's asymptotic analysis for a flat band-limited [Gaussian process](https://www.edgepedia.org/gaussian-process), a delta modulator must run at a minimum oversampling ratio \\( R = 8 \\) to reach the roughly 28 dB RMS signal-to-noise ratio required for good television transmission.[1](https://ntrs.nasa.gov/api/citations/19700001976/downloads/19700001976.pdf) Where high resolution is needed, modern practice favors sigma-delta conversion.[12](https://www.nature.com/articles/s41598-025-19272-4)\n\n## References\n\n1. [Delta-modulation technical report chapter (NASA, 1970)](https://ntrs.nasa.gov/api/citations/19700001976/downloads/19700001976.pdf)\n2. [TIMS Experiment Manual: Delta Modulation (Vol D1)](https://www.eng.auburn.edu/~troppel/courses/TIMS-manuals-r5/TIMS%20Experiment%20Manuals/Student_Text/Vol-D1/D1-13.pdf)\n3. [Continuously Variable Slope Delta Modulation: A Tutorial (MXCom)](https://www.raffia.ch/content/datasheets/volume01/Tutorial_DeltaMod_CVSD_MxCom.pdf)\n4. [Delta modulation | IEEE Technology Navigator](https://technav.ieee.org/topic/delta-modulation/)\n5. [Motorola AN1544: Delta Modulation / CVSD application note](https://www.raffia.ch/content/datasheets/volume01/AN1544_DeltaMod_CVSD_Motorola.pdf)\n6. [Comparison of LDM, CVSD, and ADPCM - MATLAB & Simulink](https://www.mathworks.com/help/dsp/ug/comparison-of-ldm-cvsd-and-adpcm.html)\n7. [Delta Modulation lecture notes (University of Mosul)](https://uomus.edu.iq/img/lectures21/MUCLecture_2023_6446207.pdf)\n8. [Delta modulation and DPCM lecture notes (University of Cape Town)](http://dip.ee.uct.ac.za/~nicolls/lectures/eee482f/07_dpcm.pdf)\n9. [MT-022: ADC Architectures III, Sigma-Delta ADC Basics (Analog Devices)](https://www.analog.com/media/en/training-seminars/tutorials/MT-022.pdf?doc=AN-1521.pdf)\n10. [Multimedia Communications: Differential PCM lecture notes (McMaster)](https://www.ece.mcmaster.ca/~shirani/multi12/differential.pdf)\n11. [Practical Approach of Producing Delta Modulation and Delta-Sigma Modulation (IOSR-JECE)](https://www.iosrjournals.org/iosr-jece/papers/Vol.%2011%20Issue%203/Version-2/M1103028794.pdf)\n12. [Design of low power energy efficient sigma-delta ADC for biomedical IoT applications (Scientific Reports, 2025)](https://www.nature.com/articles/s41598-025-19272-4)\n13. [A 32-channel event-based bio-signal analog front-end with adaptive delta and pulse frequency encoding (arXiv)](https://arxiv.org/html/2607.12901)\n14. [Bell System Technical Journal, 1969 vol. 2](https://www.worldradiohistory.com/Archive-Bell-System-Technical-Journal/60s/Bell-System-Technical-Journal-1969-2-Complete.pdf)\n\n---\n*Topic: Encyclopedia › Technology and the built world › Computing and digital systems › Artificial intelligence and data › Algorithms and computational methods › Numerical, string, and geometric algorithms › Fourier and signal transforms*\n\n*Initially written Sep 29, 2026 · Edited: Oct 15, 2026; Oct 21, 2026*\n\n*Copyright 2026 EdgeChat AI, a subsidiary of Biostate AI.*\n\nLicense: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license\n", "same_as": [ "https://www.eng.auburn.edu/~troppel/courses/TIMS-manuals-r5/TIMS%20Experiment%20Manuals/Student_Text/Vol-D1/D1-13.pdf" ], "url": "https://www.edgepedia.org/delta-modulation", "markdown_url": "https://www.edgepedia.org/delta-modulation.md", "license": { "name": "Edgepedia Community License 1.0", "url": "https://www.edgepedia.org/edgepedia/license", "summary": "Free with credit, commercial use included. AI training is open to everyone. For other uses, organizations over USD 100M in revenue or 100M monthly users license separately.", "spdx": "LicenseRef-Edgepedia-Community-1.0" }, "credit": "\"Delta modulation\", Edgepedia (EdgeChat), https://www.edgepedia.org/delta-modulation. Edgepedia Community License 1.0.", "credit_md": "\"[Delta modulation](https://www.edgepedia.org/delta-modulation)\", Edgepedia (EdgeChat), [https://www.edgepedia.org/delta-modulation](https://www.edgepedia.org/delta-modulation). [Edgepedia Community License 1.0](https://www.edgepedia.org/edgepedia/license).", "credit_html": "\"Delta modulation\", Edgepedia (EdgeChat), https://www.edgepedia.org/delta-modulation. Edgepedia Community License 1.0.", "speakable": "Delta modulation is an analog-to-digital encoding method that represents a waveform with one bit per sample, sending whether the signal rose or fell; it underlies sigma-delta converters." }