A finite duration discrete-time signal x[n] is obtained by sampling the continuous-time signal x(t) = cos (200πt) at sampling instants t = n/400, n = 0, 1, …, 7. The 8-point discrete Fourier transform (DFT) of x[n] is defined as:$X\left[ k \right] = \mathop \sum \limits_{n = 0}^7 x\left[ n \right]{e^{ - j\frac{{\pi kn}}{4}}},\;k = 0,\;1,\; \ldots ,\;7.$Which one of the following statements is TRUE?

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TuteeHUB · Accepted Answer

Only X[3] and X[5] are non-zero

TuteeHUB · Answer

All X[k] are non-zero

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Only X[4] is non-zero

TuteeHUB · Answer

Only X[2] and X[6] are non-zero

1.	A finite duration discrete-time signal x[n] is obtained by sampling the continuous-time signal x(t) = cos (200πt) at sampling instants t = n/400, n = 0, 1, …, 7. The 8-point discrete Fourier transform (DFT) of x[n] is defined as:\(X\left[ k \right] = \mathop \sum \limits_{n = 0}^7 x\left[ n \right]{e^{ - j\frac{{\pi kn}}{4}}},\;k = 0,\;1,\; \ldots ,\;7.\)Which one of the following statements is TRUE?
A.	All X[k] are non-zero
B.	Only X[4] is non-zero
C.	Only X[2] and X[6] are non-zero
D.	Only X[3] and X[5] are non-zero
Answer» D. Only X[3] and X[5] are non-zero

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