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).
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