Question: Suppose x[n] is a periodic sequence with period N. Then x[n] is also periodic with 3N. Let X[k] denote the DFS coefficients of x[n] considered

Suppose x[n] is a periodic sequence with period N. Then x[n] is also periodic with 3N. Let X[k] denote the DFS coefficients of x[n] considered as a periodic sequence with period N, and let X₃[k]denote the DFS coefficients of x[n]?considered as a periodic sequence with period 3N.

(a) Express X₃[k] in terms of X[k].

(b) By explicitly calculating X[k] and X₃[k], verify your result in part (a) when x[n] is as given in Figure

* [n]. N = 2 2 29 -2 -1 0 1 2

* [n]. N = 2 2 29 -2 -1 0 1 2 3 4 5 6 7

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