Problem # 1.0 12 A zero mean, WSS, stochastic sequence has a power spectral density of the form: Pix(e " ) = 2.25. 5 -4 cos w 10 - 6 cos w For this sequence: 1. Show that this sequence satisfies the conditions for spectral factorization, i.e., show that it is real, positive, and bounded. 2. Using analytic continuation determine the power spectral density Pry (2) in the complex z-plane and determine the appropriate region of convergence. Determine the factors involved in the PSD factorization of this process clearly indicating the corresponding regions of convergence for each of the factors. 3. Determine the autocorrelation sequence rix and the average power Pave of the sequence r[n]. 4. Determine the system function #white (2) of the whitening system that converts the sequence an into the white, innovations process v[n]. Is this system unique. If not is there another system that accomplishes the same task? Justify your answer properly