Question: Consider the finite-length sequence x[n] = 2[n] + [n 1] + [n 3]. We perform the following operation on this sequence: (i) We

Consider the finite-length sequence

x[n] = 2δ[n] + δ[n – 1] + [n – 3].

 We perform the following operation on this sequence:

(i) We compute the five-point DFT X[k].

(ii) We compute a five-point inverse DFT of Y[k] = X[k]2 to obtain a sequence y[n].

(a) Determine the sequence y[n] for n = 0, 1, 2, 3, 4.

(b) If N-point DFTs are used in the two-step procedure, how should we choose N so that y[n] = x [n]* x[n] for 0 ≤ n ≤ N – 1?

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