The periodogram I(ω) of a discrete-time random signal x[n] was defined in Eq. (10.67) as
where V (ejω) is the DTFT of the finite-length sequence v[n] = w[n]x[n], with w[n] a finite-length window sequence of length L, and U is a normalizing constant. Assume that x[n] and w[n] are real. Show that the periodogram is also equal to 1/LU times the Fourier transform of the aperiodic autocorrelation sequence of v[n]; i.e.,
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