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# Differential Pulse Code Modulation (DPCM)

For the signals which does not change rapidly from one sample to next sample, the PCM scheme is not preferred.

Differential Pulse Code Modulation (DPCM)

For the signals which does not change rapidly from one sample to next sample, the PCM scheme is not preferred. When such highly correlated samples are encoded the resulting encoded signal contains redundant information. By removing this redundancy before encoding an efficient coded signal can be obtained. One of such scheme is the DPCM technique. By knowing the past behavior of a signal up to a certain point in time, it is possible to make some inference about the future values. The transmitter and receiver of the DPCM scheme is shown in the below fig.respectively. Transmitter: Let x(t) be the signal to be sampled and x(nTs) be its samples. In this scheme the input to the quantizer is a signal. where x^(nTs) is the prediction for unquantized sample x(nTs). This predicted value is produced by using a predictor whose input, consists of a quantized versions of the input signal x(nTs). The signal e(nTs) is called the prediction error.

By encoding the quantizer output, in this method, we obtain a modified version of the PCM called differential pulse code modulation (DPCM).

Quantizer output,

v(nTs) = Q[e(nTs)]

= e(nTs) + q(nTs) ---- (3.32)

Predictor input is the sum of quantizer output and predictor output, u(nTs) = x^(nTs) + v(nTs) ---- (3.33)

Using 3.32 in 3.33,

u(nTs) = x^(nTs) + e(nTs) + q(nTs) ----(3.34)

u(nTs) = x(nTs) + q(nTs) ----(3.35)

The receiver consists of a decoder to reconstruct the quantized error signal. The quantized version of the original input is reconstructed from the decoder output using the same predictor as used in the transmitter. In the absence of noise the encoded signal at the receiver input is identical to the encoded signal at the transmitter output. Correspondingly the receive output is equal to u(nTs), which differs from the input x(nts) only by the quantizing error q(nTs).  Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail
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