DFT of real sequences with odd harmonics only Let x(n) be an N-point real sequence with...

DFT of real sequences with odd harmonics only Let x(n) be an N-point real sequence with N-point DFT X(k) (N even). In addition, x(n) satisfies the following symmetry property:

that is the upper half of the sequence is the negative of the lower halt

(a) Show that

X(k) = 0, k even

that is, the sequence has a spectrum with odd harmonics.

(b) Show that the values of this odd-harmonic spectrum can be computed by evaluating the N/2-point DFT of a complex modulated version of the original sequence x(n).