Question: Computation of the even and odd harmonics using the DFT Let x(n) be an N-point sequence with an n-point DFT X(k) (N even) (a) Consider

Computation of the even and odd harmonics using the DFT Let x(n) be an N-point sequence with an n-point DFT X(k) (N even)

(a) Consider the time-aliased sequence. What is the relationship between the M-point DFT Y(k) of y(n) and the Fourier transform X(?) of x(n)?

x(n +IM). 0

(b) Let, and show that X(k) = Y(k/2), k = 2, 4, . . . , N ? 2?

(c) Use the results in parts (a) and (b) to develop a produce that computes the odd harmonics of X(k) using an N/2-point DFT.

x(n +IM). 0

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