A continuous time signal x c (t) cos( 0 t) is sampled with period T to produce the sequence x n x c (nT) An N point rectangular window is applied to x n for 0, 1, N1, and X k , for k 0, 1, N 1, is the N point DFT of the resulting sequence (a) Assuming that 0 , N, and k 0 are fixed, how should T be chosen so that X k 0 and X N k 0 are nonzero and X k 0 for all other values of k (b) Is your answer unique If nor, give another value of T that satisfies the conditions of part (a)

Question: A continuous-time signal x c (t) = cos( 0 t) is sampled with period T to produce the sequence x[n] = x c (nT). An

A continuous-time signal x_c(t) = cos(Ω₀t) is sampled with period T to produce the sequence x[n] = x_c(nT). An N-point rectangular window is applied to x[n] for 0, 1, … N−1, and X[k], for k = 0, 1,…. N – 1, is the N-point DFT of the resulting sequence.

(a) Assuming that Ω₀, N, and k₀ are fixed, how should T be chosen so that X[k₀] and X[N – k₀] are nonzero and X[k] = 0 for all other values of k?

(b) Is your answer unique? If nor, give another value of T that satisfies the conditions of part (a).

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