Solution:

The polyphase structures for the decimators and the interpolator require the same number of filter operations as the efficient direct form structures.

$\rightarrow$ Consider a system function $H[z]$ of length 9 $H[z]=h[0]+h[1] z^{-1}+h[z] z^{-2}+h[3] z^{-3}+h[4] z^{-4}$ $+h[5] z^{-5}+h[6] z^{-6}+h[7] z^{-7}+h[8] z^{-8}$

$\longrightarrow$ This can be expressed as a sum …