The periodogram I(?) if a discrete-time random signal x[n] was defined in Eq. (10.52) as?

I(?) = 1/LU |V(e^j?)|²,

where V(e^j?) is the discrete-time Fourier transform 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.

Show that the periodogram is also equal to 1/LU times the Fourier transform of the aperiodic autocorrelation sequence of v[n]; i.e.,

Transcribed Image Text:

L-I . 2 I(@) = Cer[m]e jum Σ LU me-(1-1) where L-1 Cuu[m] = vln]v[n + m]. %3D n=0