A finite duration discrete-time signal x(n) is obtained by sampling the continuous-time signal x(t) = cos(200πt) at sampling instant t = n/400, n = 0, 1, . . . , 7. The 8-point discrete Fourier transform (DFT) of x(n) is defined as $$X\left[ k \right] = \sum\limits_{n = 0}^7 {x\left[ n \right]{e^{\frac{{ - j\pi kn}}{4}}},\,k = 0,\,1,\,.....,\,7} $$
Which one of the following statements is true?
A. Only X(2) and X(6) are non-zero
B. Only X(3) and X(5) are non-zero
C. All X(k) are non-zero
D. Only X(4) is non-zero
Answer: Option A
This Question Belongs to Electronics And Communications Engineering >> Signal Processing
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