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).
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