Computation of the even and odd harmonics using the D F7: Let x(n) be an N -point sequen...

Computation of the even and odd harmonics using the D F7: 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 (ω) of x(n)? (b) Let

and

y(n) 4-L> Y(k) N/2 Show that X(k) = Y (k/2), k = 2, 4, ... , N - 2.

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