In Section 9.1.2, we used the fact that WN−kN= 1 to derive a recurrence algorithm for co...

In Section 9.1.2, we used the fact that W_N^−kN= 1 to derive a recurrence algorithm for computing a specific DFT value X[k] for a finite-length sequence x[n], n = 0, 1, . . . , N −1.

(a) Using the fact , show thatX[N−k] can be obtained as the output after N iterations of the difference equation depicted in Figure P9.21-1. That is, show that

X[N − k] = y_k[N].

(b) Show that X[N − k] is also equal to the output after N iterations of the difference equation depicted in Figure P9.21-2. Note that the system of Figure P9.21-2 has the same poles as the system in Figure 9.2, but the coefficient required to implement

the complex zero in Figure P9.21-2 is the complex conjugate of the corresponding coefficient in Figure 9.2; i.e.,