(a) The autocorrelation function, ryy[m] of a zero-mean wide-sense stationary random...

(a) The autocorrelation function, ryy[m] of a zero-mean wide-sense stationary random process y[n] is given. In terms of r_yy[m], write the Yule–Walker equations that result from modeling the random process as the response to a white noise sequence of a

3rd-order all-pole model with system function

(b) A random process v[n] is the output of the system shown in Figure P11.12-1, where x[n] and z[n] are independent, unit variance, zero mean, white noise signals, and h[n] = δ[n − 1] + 1/2 δ[n − 2]. Find r_vv[m], the autocorrelation of v[n].

(c) Random process y₁[n] is the output of the system shown in Figure P11.12-2, where x[n] and z[n] are independent, unit variance, zero-mean, white noise signals, and

The same a and b as found in part (a) are used for all-pole modeling of y₁[n]. The inverse modeling error, w₁[n], is the output of the system shown in Figure P11.12-3. Is w₁[n] white? Is w₁[n] zero mean? Explain.

(d) What is the variance of w₁[n]?