The purpose of this problem is to show that the polynomials which are the system functi...

The purpose of this problem is to show that the polynomials which are the system functions of the forward prediction-error filters of order m, m = 0, 1, . . . , p, can be interpreted as orthogonal on the unit circle. Toward this end, suppose that is the power spectral density of a zero-mean random process {x(n)} and let be the system functions of the corresponding prediction-error filters. Show that the polynomials satisfy the orthogonality property