Type II Polyphase Decomposition

The preceding polyphase decomposition of $H(z)$ into $N$ channels

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

can be termed a ``Type I'' polyphase decomposition.

In the ``Type II'', or reverse polyphase decomposition, the powers of $z$ progress in the opposite direction:

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

We will see later that we need Type I for analysis filters and Type II for synthesis filters in a ``perfect reconstruction filter bank''.