Consider a signal s[n] that we model as the impulse response of an all-pole system of or...

Consider a signal s[n] that we model as the impulse response of an all-pole system of order p. Denote the system function of the p^th-order all-pole model as H^(p)(z) and the corresponding impulse response as h^(p)(z). Denote the inverse of H^(p)(z) as H^(p)_inv (z) =1/H^(p)(z). The corresponding impulse response is given by

where g^(p)[n] is the output of the filter when the input is s[n].

(a) Figure P11.9 depicts a signal flow graph of the lattice filter implementation of the impulse response at n = 1.

(b) Suppose we now wish to model the signal s[n] as the impulse response of a 2^nd-order all-pole filter. Draw a signal flow graph of the lattice filter implementation of

(c) Determine the system function of the 2^nd-order all-pole filter.