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GATE EC 2020 Set 1 — Question 39

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MCQ+2 / -0.67MediumDFT & FFTDiscrete-Time SignalsSignals & Systems

Signals & Systems → Discrete-Time Signals → DFT & FFT

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A finite duration discrete-time signal x[n]x[n] is obtained by sampling the continuous-time signal x(t)=cos⁡(200πt)x(t) = \cos(200\pi t) at sampling instants t=n/400,n=0,1,…,7t = n/400, n = 0, 1, \dots, 7. The 8-point discrete Fourier transform (DFT) of x[n]x[n] is defined asX[k]=∑n=07x[n]e−jπkn4,k=0,1,…,7.X[k] = \sum_{n=0}^{7} x[n] e^{-j \frac{\pi kn}{4}}, \quad k = 0, 1, \dots, 7.Which one of the following statements is TRUE?
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