# DPCM

**DPCM** or **differential pulse-code modulation** is a
signal encoder that uses the baseline of 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.

If the input is a continuous-time analog signal, it needs to be 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, quantize them; calculate the difference between the first one and the next; the output is the difference, and it can be further entropy coded.
- 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.^{[1]}

Following are the diagrams of the encoder and decoder of the two versions commented:

## Contents[hide] |

## [edit] Option 1: difference between two consecutive samples

The encoder makes the role of differentiation (the quantizer should precede the difference, unlike shown in the figure), while the decoder serves as an accumulator.

The quantifier (Q) reduces the number of bits while the reverse
quantifier (*Q* ^{− 1})
recovers the number of bits of the original initial discrete signal.

## [edit] Option 2: Analysis-by-synthesis

Incorporation of the decoder inside the encoder

## [edit] See also

- Adaptive DPCM (ADPCM)
- Delta modulation, a special case of DPCM where the
differences e
_{Q}[n] are represented with 1 bit as ±Δ - Pulse-code modulation (PCM)
- Pulse modulation methods
- Sigma-delta modulation

## [edit] References

**^**U.S. patent 2605361, C. Chapin Cutler, "Differential Quantization of Communication Signals," filed June 29, 1950, issued July 29, 1952