The butterfly flow graph in figure can be used to compute the DFT of a sequence of
Question:
The butterfly flow graph in figure can be used to compute the DFT of a sequence of length N = 2v ?in-place,? i.e., using a single array of complex-valued registers. Assume this array of registers A[?] is indexed on 0 ? I ? N ? 1. The input sequence is initially stored in A[?] in bit-reversed order. The array is then processed by v stages of butterflies. Each butterfly takes two array elements A[?0] and A[?1] as inputs, then stores its outputs into those same array locations. The values of ?0?and ?1?depend on the stage number and the location of the butterfly in the signal flow graph. The stages of the computation are indexed by m = 1, ,?, v.
(a)?What is |?1 ? ?0| as a function of the stage number m??
(b) Many stages contain butterflies with the same ?twiddle? factor WrN. ?For these stages, how far apart ate the values of ?0 for the butterflies with the same WrN?
Transcribed Image Text:
(m - 1)st stage mth stage -1
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