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Solutions of posed Qs on ADC, Sampling and Transmission

An audio signal has frequencies between 100 Hz and 12 kHz. It is sampled and converted to a digital bit stream using an 8 bit A/D converter. The digital signal is sent to a receiver that converts the signal back to its original analog form.

a. Calculate the lowest sampling frequency that can be used in practice.

b. The audio signal is sampled at 32 kHz and transmitted as a serial bit stream. If no additional bits are added, calculate the bit rate of the resulting digital signal.

c. The digital signal is transmitted in packets that contain 8 digital words of 8 bits/word. If the packets are transmitted as a continuous bit stream, calculate the duration of a packet.

d. The packets in part (c) above are multiplexed with a second identical bit stream and transmitted as a continuous serial bit stream. What is the bit rate now?

e. Calculate the approximate quantization S/N ratio in the baseband audio signal at the receiver output (after the DAC and LPF).

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Solution Preview

a. The lowest sampling frequency is twice the Nyquist rate or another way of saying this is twice the highest
frequency in the baseband signal. The highest frequency component in the baseband is 12 kHz,
implying that the lowest sampling frequency to be used for faithful reproduction is f(s).

f(s) = 2 x 12 kHz = 24 kHz

b. Audio is sampled at f(s) = 32 kHz so this implies that there are 32,000 samples each second. As each
sample contains m = 8 bits

The bit rate R = m*f(s) = 8 x 32000 = 256 kbps

c. 1 packet contains ...

Solution Summary

Details of a baseband audio signal are presented and it is shown how to determine the minimum sampling frequency for faithful reporduction. Based on intial information the bit rate of the digitized stream is determined, the packet size and the Quantization SNR