Suppose that a finite-length sequence x[n] has the N-point DFT X [k], and suppose that the sequence satisfies the symmetry condition x[n] = - x[((n + N/2)) N], 0 = n = N - 1, where N is even and x [n] is complex.
(a) Show that X [k] = 0 for k = 0, 2,..., N - 2.
(b) Show how to compute the odd-indexed DFT values X[k], K = 1, 3, ..., N - 1 using only one N/2-point DFT plus a small amount of extra computation.