Suppose is a periodic sequence with period N. Then is also periodic with period 3N. Le...

Suppose is a periodic sequence with period N. Then is also periodic with period 3N. Let denote the DFS coefficients of considered as a periodic sequence with period N, and let denote the DFS coefficients of considered as a periodic sequence with period 3N.

(a) Express in terms of .

(b) By explicitly calculating and , verify your result in part (a) when is as given in Figure P8.2.