GATE EC 2017 Set 1 — Question 23
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Communications → Source Coding & Baseband Transmission → Nyquist Criterion (Zero ISI)
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Question
In a digital communication system, the overall pulse shape at the receiver before the sampler has the Fourier transform . If the symbols are transmitted at the rate of 2000 symbols per second, for which of the following cases is the inter symbol interference zero?
Correct answer
(B) [figure]
Solution
The Nyquist criterion for zero Inter-Symbol Interference (ISI) states that the sum of the shifted replicas of the Fourier transform of the pulse shape must be constant:where is the symbol rate. Given symbols/sec, we have kHz. We need to check if is constant for kHz.For Option (B), is 1 for kHz and for kHz.
In the interval kHz:
In the interval kHz:
1.For kHz, .
2.For kHz, the relevant terms are and . Since is symmetric, .
Sum .Since the sum is constant () for all , the ISI is zero. Other options do not satisfy this condition (e.g., in Option C, the sum at is , while at it is 1).Continue learning with Success Tracker
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