Consider a real-valued finite-duration sequence x[n] of length M. Specifically, x[n] = 0 for n < 0 and n > M − 1. Let X[k] denote the N-point DFT of x[n] with N ≥ M and N odd. The real part of X[k] is denoted XR[k].
(a) Determine, in terms of M, the smallest value of N that will permit X[k] to be uniquely determined from XR[k].
(b) With N satisfying the condition determined in part (a), X[k] can be expressed as the circular convolution of XR[k] with a sequence UN[k]. Determine UN[k].
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