Signal Processing for Cognitive Radios

so that (10.62b) becomes

(10.67a)

(10.67b)

(10.67c)

where (10.67c) follows from the fact that autocovariance sequence {ρ^(x)}of the signal is given by the inverse Fourier transform of its PSD function . By denoting

(10.68)

we have from (10.67c) that

(10.69a)

(10.69b)

where (10.69a) follows by defining as the DTFT of the observation sequence

(10.70)

and in (10.69b), we have defined the periodogram of the transformed observation sequence to be Ŝ_ỹ(F):

(10.71)

Comparison of (10.69b) with ( ...