Show that the Fourier transform of included in the periodogram, is periodic with period one. Show that the mean square error of the spectrum estimate is equal to the sum of the variance and the...

Show that the Fourier transform of

included in the periodogram,

is periodic with period one.

Show that the mean square error of the spectrum estimate is equal to the sum of the variance and the squared bias,

where the variance defined as

and the squared bias