Some FIR filters present a rational transfer function: (a) Show that the transfer function [H(z)=frac{left(r^{-1} z ight)^{-(M+1)}-1}{r

Some FIR filters present a rational transfer function:

(a) Show that the transfer function

\[H(z)=\frac{\left(r^{-1} z\right)^{-(M+1)}-1}{r e^{\mathrm{j} 2 \pi /(M+1)} z^{-1}-1}\]

corresponds to an FIR filter (Lyons, 2007).

(b) Determine the operation performed by such a filter.

(c) Discuss the general case when a rational transfer function corresponds to an FIR filter.