4.5 A first-order autoregressive model is generated from the white noise series wt using the generating equations xt = φxt−1 + wt, where φ, for |φ|

.

(a) Show the power spectrum of xt is given by

(b) Verify the autocovariance function of this process is

h = 0,±1,±2, . . ., by showing that the inverse transform of γx(h) is the spectrum derived in part (a).

Transcribed Image Text:

fr (w) = 1+62 20 cos(2W)*