a. A PCM system uses a uniform quantizer followed by a 7-bit binary encoder. The

Question

a. A PCM system uses a uniform quantizer followed by a 7-bit binary encoder. The bit rate of the system is equal to 70 times 10^6 bits/s. What is the maximum message bandwidth for which the system operates satisfactorily? b. A waveform x(t) = 10cos(1500 pi t + 2 pi/3) + 20cos(1000 pi t + pi/4) is to be uniformly sampled for digital transmission. i. What is the maximum allowable interval between samples that will ensure perfect signal reproduction? ii. If it is requested to reproduce 1 hour of this waveform, how many samples need to be stored.

Explanation / Answer

Answer:5a) We have bit rate R = 7 x 107 bits/s, number of bits for quantization is 7. So number of quantization level is 27 i.e 128. But by expression we have-

R = 2 x B x log2(L)

=> B = (7 x 107) / (2 x log2(128)) = 5 MHz

Answer:5b)i) We have f1 = 750 Hz, f2 = 500 Hz. So minimum sampling rate required is 2 x Max( 750, 500) Hz, i.e 1500 Hz. Hence maximum allowable time between samples is 1/1500 Second i.e 666.667 Microsecond.

Answer:5b)ii) Number of samples in one hour = 3600/one sample time interval i.e (3600x106 )/666.667 = 5400000 Samples.

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