Question #129350

The output SNR for a 10- bit PCM was found to be 30 dB. The desired SNR is 42 dB. It was decided to increase the SNR to the desired value by increasing the number of quantization levels L. Find the fractional increase in the transmission bandwidth required for this increase in L.

Expert's answer

SNR = 30 dB and N = 10

Desired value of SNR = 42 dB

To find N for 42 dB

With increase in N by 1 bit the value of SNR increases by 6 dB Therefore to increase the value of SNR by 12 dB it is necessary to increase by 2

Hence,

N = 10 + 2 = 12

fractional increase in BW

BW of PCM system = N f,

Hence BW with N = 10 is given by , BW_{10} = * 10 f = 5 f,

and BW with N = 12 is given by, BW_{12} = *12 f = 6 f,

Therefore change in BW = 6f - 5f = f,

therefore fractional change in BW = = 100% = 20%

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