Let us derive the different structures of IIR filters like FIR filters.
The IIR filter can be described by the generalized difference equation. The system function of Eq. (12.27) and it is rewritten below
From Eq. (12.66) we can conclude that the overall IIR system can be realized as a cascade of two functions H1(z) and H2(z). H1(z) represents the zeros of H(z) and it is all the zero system. H2(z) represents the poles of H(z) and it is all the pole system.
We will at first prepare the direct form structures of H1(z) and ...