Question

It has been shown that the discrete Fourier transform(DFT) of a time hltk) for (k 0,1,2, N -1). is given by V-1 k--0 Choosing N8 carry out the Cooley- Tukey formulation of FFT by following the ste below (a) Write the expressions for DFT H, in terms of hita) and the inverse DFT ht) in terms of f, for N = 8. (b) Define ". ear/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 summation( 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. Carry out the third step summation and express the result in matrix forin. (i) Draw a sketch of the signal fow st.arting with htte) and event ually arriving at (i) Summarize and discuss your results and findings. 1 - Phew!) Now you may want to try the whole procedure with N 16 Phew!) Now you (k)(Optional

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Answer 1

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