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LUCKY_DIMON [66]
3 years ago
9

An analog signal is sampled, quantized, and encoded into a binary PCM wave. The number of representation levels used is 128. A s

ynchronizing pulse is added at the end of each code word representing a sample of the analog signal. The resulting PCM wave is transmitted over a channel of bandwidth 12 kHz using a quaternary PAM system with raised-cosine spectrum. The roll-off factor is unity.
a. Find the rate (b/s) at which information is transmitted through the channel.
b. Find the rate at which the analog signal is sampled. What is the maximum possible value for the highest frequency component of the analog signal?

Engineering
2 answers:
Rus_ich [418]3 years ago
7 0

Given Information:

Quantizing level = 128

bandwidth = 12 kHz

Required Information:

a) data rate = ?

b) sampling rate = ?

Answer:

a) data rate = 24,000 bits/s

b) sampling rate = 3 kHz

Explanation:

a. Find the rate (b/s) at which information is transmitted through the channel.

The data rate is given by

data rate = 2*Bandwidth

data rate = 2*12,000

data rate = 24,000 bits/s

b. Find the rate at which the analog signal is sampled. What is the maximum possible value for the highest frequency component of the analog signal?

Quantizing level = 128

The corresponding number of bits transmitted per sample is given by

Log₂(128) = 7 bits

We are given that a synchronizing pulse is added at the end of each code word representing a sample of the analog signal, therefore, total number of bits are

7 bits + 1 bit = 8 bits

Therefore, the sample rate is

sampling rate = data rate/number of bits

sampling rate = 24,000/8

sampling rate = 3,000 Hz

sampling rate = 3 kHz

According to the Nyquist criteria the sampling rate must be at least twice of the highest frequency component of the input signal, so

sampling rate = 2*f

3 kHz = 2*f

f = 3 kHz/2

f = 1.5 kHz

professor190 [17]3 years ago
3 0

Answer:

a. 12 kbps

b. 428.6 Hz

Explanation:

Please kindly check attachment for the step by step solution of the given problem.

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