A continuous-time signal xc(t) = cos(t) is sampled with period T to produce the sequence...

A continuous-time signal xc(t) = cos(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, . . . , N−1, and X[k], for k = 0, 1, . . . , N − 1, is the N-point DFT of the resulting sequence.

(a) Assuming that , 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 not, give another value of T that satisfies the conditions of part (a).