Figure 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 [?] and C [?], determine and sketch the array sequence D[r], r = 0, 1?. 7. If the input sequence is x[n] = (? w_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 .?

Transcribed Image Text:

Cj0] B[0] D[0] A [0] o CI] B[1] A[1]o D[1] B[2] w C12] A[2] o D{2] B[3] W C[3] A[3] o D[3] C[4] W B[4] A[4] o- D[4] BIS] A[5] o M Isl.ɔ D[5] C16| W B[6] W D161 A[6] o D(6] B(7) W -1 C[7] w A[7]o D[7] -1