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# Sampling frequency and bit rate of transmission

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The output of a video surveillance camera is an analog signal with a bandwidth that extends from 0 Hz to 1.5 MHz. The signal is sampled at 1.2 times its Nyquist rate.

The resulting PAM signal is converted to 6 bit digital words with an analog to digital converter and the words are transmitted serially over a twisted pair used as the cable for data transmission.

a. What is the sampling frequency?

b. What is bit rate of the transmission on the twisted pair?

c. If the digital outputs of three identical video cameras are combined onto a single cable using time division multiplexing, what is the bit rate on the cable?

https://brainmass.com/engineering/electrical-engineering/sampling-frequency-and-bit-rate-of-transmission-345014

#### Solution Preview

Given, bandwidth of analog signal = B = 1.5 MHz

So, Nyquist sampling rate for this signal = fN = 2B = 2*1.5 MHz = 3 MHz or 3M samples/second

a. Since the signal is sampled at 1.2 times its Nyquist rate, the sampling frequency = 1.2 fN = 1.2*3 ...

#### Solution Summary

In part (c), solution assumes that the Time Division Multiplexer reads data from each video camera at same rate as the sampling frequency.

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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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