Differential pulse-code modulation (DPCM) is a signal encoder that uses the baseline of pulse-code modulation

Pulse-code modulation

Pulse-code modulation is a method used to digitally represent sampled analog signals. It is the standard form for digital audio in computers and various Blu-ray, Compact Disc and DVD formats, as well as other uses such as digital telephone systems...

 (PCM) but adds some functionalities based on the prediction of the samples of the signal. The input can be an analog signal

Analog signal

An analog or analogue signal is any continuous signal for which the time varying feature of the signal is a representation of some other time varying quantity, i.e., analogous to another time varying signal. It differs from a digital signal in terms of small fluctuations in the signal which are...

 or a digital signal

Digital signal

A digital signal is a physical signal that is a representation of a sequence of discrete values , for example of an arbitrary bit stream, or of a digitized analog signal...

.

If the input is a continuous-time analog signal, it needs to be sampled

Sampling (signal processing)

In signal processing, sampling is the reduction of a continuous signal to a discrete signal. A common example is the conversion of a sound wave to a sequence of samples ....

 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
  Quantization (signal processing)
  Quantization, in mathematics and digital signal processing, is the process of mapping a large set of input values to a smaller set – such as rounding values to some unit of precision. A device or algorithmic function that performs quantization is called a quantizer. The error introduced by...
  
   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

C. Chapin Cutler

Cassius Chapin Cutler was an American electrical engineer at Bell Labs. His notable achievements include the invention of the corrugated waveguide and differential pulse-code modulation .-Biography:...

 at Bell Labs

Bell Labs

Bell Laboratories is the research and development subsidiary of the French-owned Alcatel-Lucent and previously of the American Telephone & Telegraph Company , half-owned through its Western Electric manufacturing subsidiary.Bell Laboratories operates its...

 in 1950; his patent includes both methods.

Option 1: difference between two consecutive quantized samples

The encoder makes the role 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 quanitizer is uniform, the decoder regenerates the differences implicitly, as in this simple diagram that Cutler showed:

See also

• Adaptive DPCM
  Adaptive DPCM
  Adaptive differential pulse-code modulation is a variant of differential pulse-code modulation that varies the size of the quantization step, to allow further reduction of the required bandwidth for a given signal-to-noise ratio....
  
  
• Delta modulation
  Delta modulation
  Delta modulation is an analog-to-digital and digital-to-analog signal conversion technique used for transmission of voice information where quality is not of primary importance. DM is the simplest form of differential pulse-code modulation where the difference between successive samples is encoded...
  
  , a special case of DPCM where the differences e_Q[n] are represented with 1 bit as ±Δ
• Pulse modulation methods
• Delta-sigma modulation
  Delta-sigma modulation
  Delta-sigma modulation is a method for encoding high-resolution or analog signals into lower-resolution digital signals. The conversion is done using error feedback, where the difference between the two signals is measured and used to improve the conversion...