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If N=LM, then what is the value of WN^mqL?

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If N=LM, then what is the value of WN^mqL?

(a) WM^mq

(b) WL^mq

(c) WN^mq

(d) None of the mentioned

I got this question in my homework.

Question is taken from Efficient Computation of DFT FFT Algorithms topic in section DFT Efficient Computation – Fast Fourier Transform Algorithms of Digital Signal Processing

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The correct choice is (a) WM^mq

The explanation is: We know that if N=LM, then WN^mqL = WN/L^mq = WM^mq.

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