Question
Download Solution PDFThe butterfly in fig. is taken from radix 2 decimation in time FFT with N = 32. Assume that the five stages of the signal flow graph are indexed by m = 1, 2, 3, 4, 5, where 5 is the last stage. Which of the five stages has butterflies of this form?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
In a radix-2 Decimation-in-Time (DIT) FFT algorithm, the computation is broken into multiple stages of "butterfly" operations. Each butterfly computes a pair of values using inputs and a complex multiplier called a twiddle factor.
The twiddle factor is given by:
As the FFT progresses through stages from m = 1 to m = log2(N), the values of
Given:
Total number of points:
The butterfly shown involves twiddle factor
Observation:
The usage of
Such butterflies are observed in the last two stages of a 5-stage FFT flow graph: m = 4 and m = 5.
Hence, the correct answer is option 2
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