Evaluate numerically and include units where applicable. 10 audio signal are to

Question

Evaluate numerically and include units where applicable. 10 audio signal are to be sampled, quantized, multiplexed, and transmuted using M - ary PCM. Each audio signal has effective bandwidth B = 5kHz and is sampled at the Nyquist rate. Each signal is quantized using L = 2^6 levels. The channel has 100 kHz bandwidth. a) Determine the minimum number of pulse levels, m, that should be used to transmit the multiplexed M - ary PCM data Minimum m = b) Using the result from a), determine the minimum data rate to transmit the multiplexed M - ary PCM signal. Minimum Data Rate R_M - ary = __ c) Briefly discuss the impact on 2 factors when using M - ary PCM transmission compared to binary PCM: 1) transmission bandwidth and 2) probability of detection error if the maximum pulse amplitude A_p remains the same.

Explanation / Answer

a) the minimum number of pulse levels required to transmit the multiplexed M-ary PCM data is m=10*log2(2^6)=10*6=60

b) bandwidth B=5kHz

Sampling rate S=2*5=10kHz

minimum data rate to transmit the M-ary PCM signal = 60*10kHz= 600Kbits/sec

c) transmission bandwidth of M-ary PCM is lower than that of binary PCM.

probability of detecting error in M-ary PCM is higher than that in a binary PCM as M-ary PCM has lower signal to noise ratio.

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