GATE EC 2024 Set 1 — Question 14
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Communications → Source Coding & Baseband Transmission → Nyquist Criterion (Zero ISI)
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Question
A digital communication system transmits through a noiseless bandlimited channel . The received signal at the output of the receiving filter is given by where are the symbols and is the overall system response to a single symbol. The received signal is sampled at . The Fourier transform of is . The Nyquist condition that must satisfy for zero intersymbol interference at the receiver is ______.
Correct answer
(A) Σ_(m=-∞)^(∞) X(f + (m)/(T)) = T
Solution
The Nyquist criterion for zero intersymbol interference (ISI) requires that the sampled impulse response satisfies:
In the frequency domain, this condition is equivalent to the periodic summation of the Fourier transform of the overall system response being a constant:This ensures that the aliased spectrum of the pulse is flat, which corresponds to a delta function in the time domain after sampling. Therefore, option (A) is the correct condition.
In the frequency domain, this condition is equivalent to the periodic summation of the Fourier transform of the overall system response being a constant:This ensures that the aliased spectrum of the pulse is flat, which corresponds to a delta function in the time domain after sampling. Therefore, option (A) is the correct condition.
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