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

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1/2 T.)AA )df = E6mn m.n = 0. 1..... p -1/2