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

a) bit rate=70M bits/sec;

we know that bit rate=N*f

where f=samplinf frequency

and N is given 7,on substituting in the above we will get the 'f' value which is 1 MHz

maximum signal bandwidth=(f)/2

=0.5MHz

b) from the given maximum omeg value is 1500pi,

omega=2*pi*f, then the value of f is the maximum frequency is 750Hz

minimum sampling rate=2*(maximum frequency)

=2*750

N =1500Hz

(i) maximum allowable time interval=1/N=1/1500=0.000666 sec

(ii) no of samples=( one hour)/0.000666 sec=(3600)/0.000666=5405405.4 samples

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