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ISRO (VSSC) Technical Assistant Electronics 2018 Official Paper

Option 3 : 256 kbps

Subject Test 1: Electrical Basics

3098

20 Questions
80 Marks
30 Mins

__Concept__:

The bitrate of a PCM system for an encoded signal sampled at a frequency of fs is given by:

R_{b} = m n fs

fs = Sampling frequency

n = number of bits used for encoding.

m = number of message signals

n is related to the number of quantization levels (L) as:

L = 2n

or n = log2L

__Calculation__:

Since the sampling frequency is not mentioned, we'll assume it to be sampled at the Nyquist rate, i.e.

fs = 2fm

fm = Maximum frequency present at the modulating signal.

∴ For the given band-limited signal with a frequency 4 kHz, the sampling frequency will be:

fs = 2 × 4 = 8 kHz

With L = 256, the number of bits will be:

n = log2 256 = log2 28

n = 8 bits

Now for 4 Voice signals

R_{b} = 4 × n × fs = 4 × 8 × 8000

R_{b} = 256 kbps