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# Digitizing an Audio Signal, PAM, ADC

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An audio signal has a bandwidth that extends from 100 Hz to 10 kHz. The signal is sampled to create a PAM signal and then digitized by an analog to digital converter (ADC) that has 8 bits. The digital signal is transmitted as a bit stream to a distant location where it is converted to parallel words and input to a digital to analog converter (DAC). The output of the DAC is passed through a low pass filter. You may assume the low pass filter is ideal.

a. The sampling rate is to be 1.2 times the Nyquist rate. What is the sampling frequency?

b. What is the bit rate at the output of the ADC?

c. What is the maximum bandwidth of the low pass filter at the receiving end of the link?

d. What is quantization SNR at the output of the low pass filter?

#### Solution Preview

(a) Nyquist rate {Nr} is 2x the highest frequency component {f(max)} in the Baseband signal.

Highest frequency component of Baseband extending from 100 Hz to 10 kHz is f(max) = 10 kHz

So Nr = 2*f(max)

We are told that the sampling rate {fs} is 1.2 x the Nyquist rate {Nr}, so we can say

fs = 1.2*Nr = ...

#### Solution Summary

Details of a baseband audio signal are presented such as its occupied bandwidth and the number of bits used when sampled to produce a PAM word. The sampling rate is given as 1.2 x the Nyquist rate. The solution shows how to determine

a) The minimum sampling rate based on the information

b) The bulk bit rate of the ADC

c) The maximum bandwidth requirement of the low pass filter at the recieving end of the link

d) The quantization SNR of the output of the low pass filter

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