Figure P9.7 shows the flow graph for an 8-point decimation-in-time FFT algorithm. Let x[...

Figure P9.7 shows the flow graph for an 8-point decimation-in-time FFT algorithm. Let x[n] be the sequence whose DFT is X[k]. In the flow graph, A[·],B[·],C[·], and D[·] represent separate arrays that are indexed consecutively in the same order as the indicated nodes.

(a) Specify how the elements of the sequence x[n] should be placed in the array A[r], r = 0, 1, . . . , 7. Also, specify how the elements of the DFT sequence should be extracted from the array D[r], r = 0, 1, . . . , 7.

(b) Without determining the values in the intermediate arrays,B[·] andC[·], determine and sketch the array sequence D[r], r = 0, 1, . . . , 7, if the input sequence is x[n] = (−W_N)ⁿ, n = 0, 1, . . . , 7.

(c) Determine and sketch the sequence C[r], r = 0, 1, . . . , 7, if the output Fourier transform is X[k] = 1, k = 0, 1, . . . , 7.