Differential Pulse Code Modulation(DPCM)

By - Prof.D.P.Patnaik

Dept of ECE

Centurion University

DPCM cont..

• The samples of a signal are highly correlated with each other. This is because any signal does not change very fast. i.e its value from present sample to next sample does not differ by large amount.

• The adjacent samples of the signal carry same info with very little difference.

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• When these samples are encoded by standard PCM system, the resulting encoded signal contain redundant information.

• Consider the figure in next slide..

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01

1

10

0 1

00

10

1

10

1

10

1

10

0

01

1

01

0

01

0

01

0

Ts 2Ts 3Ts 4Ts 5Ts 6Ts 7Ts 8Ts 9Ts 10Ts 000

001

010

011

100

101

110

111

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• The signal is flat top sampled at a rate Fs Samples/sec(Higher than Nyquist rate).

• The samples are encoded using 3 bit encoder.

• The samples at 4Ts,5Ts,6Ts are encoded to same value 101.

• It means redundant info is transmitted in PCM.

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• There is also possible cases where 1st two bits are redundant & there is a change in the last bit only.

• If the redundancy is reduced, then no of bit required for transmission will reduce.

• Data rate will reduce. As a result Bandwidth requirement for the transmission will also reduce significantly.

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• This type of Digital Pulse modulation scheme is called Differential Pulse Code Modulation.

• The DPCM works on the principle of prediction.

• The value of present sample is predicted from past samples.

• The prediction may not be exact but it is very close to actual sample value.

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Quantizer Encoder

Prediction Filter

+

_

+

+

eq(nTs) x(nTs)

e(nTs)

xq(nTs)

DPCM signal

x~(nTs)

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• The sampled signal is denoted by x(nTs) & the predicted signal is denoted by x~(nTs).

• The comparator finds out the difference between the actual sample value & the predicted sample value.

• This is called error & is given by e(nTs).

e(nTs) = x(nTs)-x~(nTs)

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• The error is the difference between unquantized input sample x(nTs) & prediction of it x~(nTs).

• The predicted value is produced by using a prediction filter.

• The quantizer output signal eq(nTs) and previous prediction is added & given as input to prediction filter.

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• This signal is called xq(nTs) .This makes the prediction more close to actual sampled signal.

• It can be seen that the quantized error signal is very small & can be encoded by using small number of bits. Thus number of bits per sample is reduced.

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• The quantizer o/p can be given as

• q(nTs) is the quantization error.

• The prediction filter input is obtained by

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• By putting the value of eq(nTs)

• We can write

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• Hence prediction filter input can be written as

• Thus quantized signal is sum of original signal & quantization error.

Thank You