Official PYQ · 2020Set 1 · Q29Discrete-time SignalsMCQ2 marks

GATE EC 2020 Set 1 Q29 — Discrete-time Signals

A finite duration discrete-time signal $x[n]$ is obtained by sampling the continuous-time signal $x\left ( t \right )=\cos\left ( 200\pi t \right )$ at sampling instants $t=n/400, n=0, 1, \dots ,7.$ The $8$ -point discrete Fourier transform $\text{(DFT)}$ of $x[n]$ is defined as $X\left [ k \right ]=\sum ^{7}_{n=0}x\left [ n \right ]e^{-j\frac{\pi kn}{4}}, k=0,1, \dots ,7.$

Which one of the following statements is TRUE?

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Answer: C

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Published 10 Oct 2026

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