Consider a discrete-time signal x[n] of length N samples that was obtained by sampling a stationary, white, zero-mean continuous-time signal. It follows that
Suppose that we compute the DFT of the finite-length sequence x[n], thereby obtaining X[k] for k = 0, 1, . . . , N − 1.
(a) Determine the approximate variance of |X[k]|2 using Eqs. (10.80) and (10.81).
(b) Determine the cross-correlation between values of the DFT; i.e., determine E{X[k]X∗[r]} as a function of k and r.
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