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	{{short description\|Signal encoder}}		{{short description\|Signal encoder}}{{More citations needed\|date=November 2025}}
	{{~~One source~~\|date=~~September 2020~~}}		'''Differential pulse-code modulation''' ('''DPCM''') encodes changes between consecutive samples of a [[signal]], rather than the signal's value directly (as done in [[pulse-code modulation]]). Decoding might thus be done by some manner of [[Integral\|integrating]] DPCM samples over time. The input can be an [[analog signal]] or a [[Digital signal (signal processing)\|digital signal]].
	'''Differential pulse-code modulation''' ('''DPCM''') is a signal ~~encoder that uses~~ the ~~baseline of~~ [[pulse-code modulation]] ~~(PCM~~) ~~but adds~~ some ~~functionalities based on the prediction~~ of ~~the~~ samples ~~of the signal~~. The input can be an [[analog signal]] or a [[Digital signal (signal processing)\|digital signal]].

	If the input is a [[continuous-time]] analog signal, it needs to be [[sampling (signal processing)\|sampled]] ~~first so that~~ a [[discrete-time signal]] ~~is the input~~ to ~~the~~ DPCM ~~encoder.~~		If the input is a [[continuous-time]] analog signal, it needs to be [[sampling (signal processing)\|sampled]] to become a [[discrete-time signal]]. Two methods to encode each DPCM value are:
	* ~~Option~~ 1: ~~take the values of two consecutive samples; if they are analog samples~~, [[quantization (signal processing)\|quantize]] ~~them; calculate~~ the difference between the ~~first one~~ and ~~the next; the output is the difference~~.		* Method 1: First, [[quantization (signal processing)\|quantize]] the samples (if not quantized already). The output is the difference between the current and previous sample.
	* ~~Option~~ 2: ~~instead of taking a~~ difference ~~relative to a previous input~~ sample~~, take the difference relative to~~ the output of a local ~~model of the~~ decoder ~~process; in this option, the difference can be quantized, which allows a good way to incorporate a controlled loss in the encoding~~.		* Method 2: Quantize the difference between the current sample and the output of a local decoder.

	Applying one of these two ~~processes~~, short-term redundancy (positive correlation of nearby values) of the signal is eliminated; compression ratios on the order of 2 to 4 can be achieved if differences are subsequently [[entropy coded]] because the entropy of the difference signal is much smaller than that of the original discrete signal treated as independent samples.		Applying one of these two methods, short-term redundancy (positive correlation of nearby values) of the signal is eliminated; compression ratios on the order of 2 to 4 can be achieved if differences are subsequently [[entropy coded]], because the [[Entropy (information theory)\|entropy]] of the difference signal is much smaller than that of the original discrete signal treated as independent samples. But removing this redundancy makes the encoded signal more fragile.<ref name=":0">{{Cite journal \|last=O'Neal \|first=J. B. \|date=1965-12-27 \|title=Predictive quantizing systems (differential pulse code modulation) for the transmission of television signals \|url=https://ieeexplore.ieee.org/document/6767674 \|journal=The Bell System Technical Journal \|volume=45 \|issue=5 \|pages=689–721 \|doi=10.1002/j.1538-7305.1966.tb01052.x \|issn=0005-8580\|url-access=subscription }}</ref>

	DPCM was invented by [[C. Chapin Cutler]] at [[Bell Labs]] in 1950~~; his patent includes both methods~~.<ref>U.S. patent 2605361, C. Chapin Cutler, [https://patents.google.com/patent/US2605361 "Differential Quantization of Communication Signals"], filed June 29, 1950, issued July 29, 1952</ref>		== History ==
			[[Delta modulation]] was introduced earlier than and can be considered a special case of DPCM, as it also uses a similar [[feedback]] principle.<ref name=":0" /> DPCM was invented by [[C. Chapin Cutler]] at [[Bell Labs]] in 1950. In addition to a method that encodes the signal's [[derivative]], Cutler also describes a method that encodes the second-derivative (which reconstructs the signal using a double-integral) and a method that encodes the third-derivative of the signal (which reconstructs the signal using a triple-integral).<ref>U.S. patent 2605361, C. Chapin Cutler, [https://patents.google.com/patent/US2605361 "Differential Quantization of Communication Signals"], filed June 29, 1950, issued July 29, 1952</ref>

	==~~Option~~ 1: difference between ~~two~~ consecutive quantized samples==		=== Predictive quantizing ===
			Cutler's methods also are considered a specific case of the more general concept of predictive quantizing systems, a term sometimes used interchangeably with DPCM. A Bell Labs article by J. B. O'Neal, Jr. says, "A predictive communications system is one in which the difference between the actual signal and an estimate of the signal, based on its past, is transmitted. Both the transmitter and the receiver make an estimate or prediction of the signal's value based on the previously transmitted signal. The transmitter subtracts this prediction from the true value of the signal and transmits this difference. The receiver adds this prediction to the received difference signal yielding the true signal."<ref name=":0" />

			== Method 1: difference between consecutive quantized samples ==
	The encoder performs the function of differentiation; a quantizer precedes the differencing of adjacent quantized samples; the decoder is an accumulator, which if correctly initialized exactly recovers the quantized signal.		The encoder performs the function of differentiation; a quantizer precedes the differencing of adjacent quantized samples; the decoder is an accumulator, which if correctly initialized exactly recovers the quantized signal.

	==~~Option~~ 2: analysis by synthesis==		== Method 2: analysis by synthesis ==
	The incorporation of the decoder inside the encoder allows quantization of the differences, including nonlinear quantization, in the encoder, as long as an approximate inverse quantizer is used appropriately in the receiver. When the quantizer is uniform, the decoder regenerates the differences implicitly, as in this simple diagram that Cutler showed:		The incorporation of the decoder inside the encoder allows quantization of the differences, including nonlinear quantization, in the encoder, as long as an approximate inverse quantizer is used appropriately in the receiver. Quantization error from previous samples is accumulated via the integration, so subsequent quantizations compensate partly for prior accumulated quantization errors. When the quantizer is uniform, the decoder regenerates the differences implicitly, as in this simple diagram that Cutler showed:

	[[File:Cutler DPCM patent.png\|center\|thumb\|500px]]		[[File:Cutler DPCM patent.png\|center\|thumb\|500px]]

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{{short description|Signal encoder}}
{{One source|date=September 2020}}
'''Differential pulse-code modulation''' ('''DPCM''') is a signal encoder that uses the baseline of [[pulse-code modulation]] (PCM) but adds some functionalities based on the prediction of the samples of the signal. The input can be an [[analog signal]] or a [[Digital signal (signal processing)|digital signal]].

If the input is a [[continuous-time]] analog signal, it needs to be [[sampling (signal processing)|sampled]] first so that a [[discrete-time signal]] is the input to the DPCM encoder.
* Option 1: take the values of two consecutive samples; if they are analog samples, [[quantization (signal processing)|quantize]] them; calculate the difference between the first one and the next; the output is the difference.
* Option 2: instead of taking a difference relative to a previous input sample, take the difference relative to the output of a local model of the decoder process; in this option, the difference can be quantized, which allows a good way to incorporate a controlled loss in the encoding.

Applying one of these two processes, short-term redundancy (positive correlation of nearby values) of the signal is eliminated; compression ratios on the order of 2 to 4 can be achieved if differences are subsequently [[entropy coded]] because the entropy of the difference signal is much smaller than that of the original discrete signal treated as independent samples.

DPCM was invented by [[C. Chapin Cutler]] at [[Bell Labs]] in 1950; his patent includes both methods.<ref>U.S. patent 2605361, C. Chapin Cutler, [https://patents.google.com/patent/US2605361 "Differential Quantization of Communication Signals"], filed June 29, 1950, issued July 29, 1952</ref>

==Option 1: difference between two consecutive quantized samples==
The encoder performs the function of differentiation; a quantizer precedes the differencing of adjacent quantized samples; the decoder is an accumulator, which if correctly initialized exactly recovers the quantized signal.

==Option 2: analysis by synthesis==
The incorporation of the decoder inside the encoder allows quantization of the differences, including nonlinear quantization, in the encoder, as long as an approximate inverse quantizer is used appropriately in the receiver. When the quantizer is uniform, the decoder regenerates the differences implicitly, as in this simple diagram that Cutler showed:

[[File:Cutler DPCM patent.png|center|thumb|500px]]

==See also==
* [[Adaptive differential pulse-code modulation]]
* [[Delta modulation]], a special case of DPCM where the differences e<sub>Q</sub>[n] are represented with 1 bit as ±Δ
* [[Pulse modulation methods]]
* [[Delta-sigma modulation]]

==References==
<references />

{{Compression methods}}

[[Category:Telephony signals]]
[[Category:Data compression]]

Differential pulse-code modulation - Revision history

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