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A music signal has a bandwidth of 50 Hz to 10 kHz. The signal is sampled, converted to a serial bit stream, transmitted over a digital radio link, and recovered as an analog signal at the receiver.

a. What is the sampling rate for this signal if sampling occurs at 1.2 times the Nyquist rate?

b. The ADC used at the transmit end of the link has 12 bits. What is the link serial bit rate?

c. After the signal has been converted back to analog form by the DAC in the receiver, it is passed through a low pass filter. If the filter is an ideal brick wall LPF, what is the maximum frequency the filter should pass? With a real filter, what cut off frequency should it have?

d. What is the quantization signal to noise ratio SNRQ at the receiver output?

e. If the SNRQ were to be raised to 96 dB, how many bits would the ADC and DAC need? What would be the bit rate on the serial link?

#### Solution Preview

a. Nyquist Rate = 2* Bandwidth
For Base Band Signals Bandwidth is upper bound i.e. 10kHz in this case
So, Nyquist Rate = 2* 10kHz=20kHz
Sampling Rate =1.2*Nyquist Rate= 1.2*20kHz=24kHz

b. ADC has 12 bits, so while transmitting bits serially, 12 bits will be sent for one sample
Serial bit rate=12*24kHz=288kHz

c. Ideal brick ...

#### Solution Summary

This solution addresses a sequence of problems related to the music signal transmitted over a digital radio link. Sampling rate requirement, ADC choice and link serial bit rate are calculated. The filter cut-off frequency and SNRQ at the receiver output as well as the variation in SNRQ and its effect on the ADC/DAC are analyzed.

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