Consider an arbitrary digital filter with transfer function (a) Perform a two...

Consider an arbitrary digital filter with transfer function

(a) Perform a two-component polyphase decomposition of H(z) by grouping the even-numbered samples and the odd-numbered samples Thus show that H (z) can be expressed as

and determine

(b) Generalize the result in part (a) by showing that H(z) can be decomposed into a D-component polyphase filter structure with transfer function

Determine

(c) For the IIR filter with transfer function

determine for the two-component decomposition.