Question

shown that the discrete Pourier transform(DFT) of a time-varying process h(4) for (k = 0, 1, 2, . .. ,N-1), is given by N-1 Choosing N-8 carry out the Cooley-Tukey formulation of FFT by following the steps below. (a) Write the expressions for DFT H, in terms of hite) and the inverse DFT h(te) in terms of H, for N 8 (b) Define W-ca/N and rewrite (a) using W (c) Express (b) in matrix form. (d) Express n and k in binary form. (e) Write the DFT of (b) in 3-step sunnmation(Why? 8-2" with r = 3 !!!). (f) Carry out the first-step summation and express the result in matrix form (g) Carry out the second-step summation and express the result in matrix form (h) Carry out the third-step summation and express the result in matrix form. (i) Draw a sketch of the signal flow starting with hite) and eventually arriving at Hs) i) Summarize and discuss your results and findings (k) (Optional - Phew!) Now you may want to try the whole procedure with N-16 want to solve from (d) to the end. please help

Answer 1

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Ummtiun 2 n sunmton isa shounin Bucttet to vedue mmaien