Consider a discrete-time signal x[n] of length N samples that was obtained by sampling a...

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.