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Analysis of digitally sampled PCM audio signal

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An audio signal has a frequency range from 50 Hz to 20 kHz. The signal is sampled, digitized and recorded on magnetic tape as a PCM signal.

a. Assuming that ideal filters are available, what is the lowest frequency at which the signal can be sampled and subsequently recovered in its analog form without distortion using a low pass filter?

b. The audio signal is sampled at a frequency of 50 kHz and converted to a serial bit stream using a 12 bit analog to digital converter (ADC). What is the bit rate of the digital signal that is recorded on the magnetic tape?

c. When the analog signal is recovered, aliasing can occur if the low pass filter in the receiver is not correct. What specific criterion must the low pass filter meet to avoid aliasing?

d. The digital signal is replayed on a magnetic tape player and converted back to an analog signal using a digital to analog converter. What is the quantization signal to noise ratio (SNR) of the analog signal?

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Solution Preview

a. Lowest frequency that the signal can be sampled at and provide integral reproduction is, by Nyquist, 2 times the highest frequency component in the baseband signal i.e.

fs(min) = 2 x 20 kHz = 40 kHz

b. If the sampling frequency is fs = 50 kHz = 5 x 10^4 Hz and the number of bits per sample m is 12
(specification of the ADC given) then bit rate of the digital signal R is given by

R = ...

Solution Summary

A digitially sampled PCM audio signal is analysed to determine the mimimal sampling frequency required for zero distortion in the output waveform from know input baseband criteria. The bit rate of the outgoing stream is determined from known inputs. Requirements of the anti aliasing low pass filter are determined for the conversion of the PCM signal back to baseband, Finally the quantisation SNR is determined for the PCM stream

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