Consider a stable LTI system with impulse response h[n] and all-pole system function...

Consider a stable LTI system with impulse response h[n] and all-pole system function

Such all-pole systems arise in linear-predictive analysis. It is of interest to compute the complex cepstrum directly from the coefficients of H(z).

(a) Determine ˆh[0].

(b) Show that

With the relations in parts (a) and (b), the complex cepstrum can be computed without phase unwrapping and without solving for the roots of the denominator of H(z).