Consider the system described by the difference equation
y(n) = ay(n – 1) – ax(n) + x (n – 1)
(a) Show that it is all-pass.
(b) Obtain the direct form II realization of the system
(c) If you quantize the coefficients of the system in part (b), is it still all-pass?
(d) Obtain a realization by rewriting the difference equation as
y(n) = a[y(n – 1) – x(n)] + x(n – 1)
(e) If you quantize the coefficients of the system in part (d), is it still all-pass?