Type II Polyphase Decomposition

The polyphase decomposition of $H(z)$ into $N$ channels in (11.11) may be termed a ``type I'' polyphase decomposition. In the ``type II'', or reverse polyphase decomposition, the powers of $z$ progress in the opposite direction:

$$H(z) \eqsp \sum_{l=0}^{N-1} z^{-(N-l-1)} R_{l}(z^{N})$$ (12.14)

We will see that we need type I for analysis filter banks and type II for synthesis filter banks in a general ``perfect reconstruction filter bank'' analysis/synthesis system.