Paraunitary Filter Banks

Paraunitary filter banks form an interesting subset of perfect reconstruction (PR) filter banks. We saw above that we get a PR filter bank whenever the synthesis polyphase matrix $\bold{R}(z)$ times the analysis polyphase matrix $\bold{E}(z)$ is the identity matrix $\bold{I}$, i.e., when

$$\bold{P}(z) \isdef \bold{R}(z)\bold{E}(z) = \bold{I}.$$

In particular, if $\bold{R}(z)$ is the paraconjugate of $\bold{E}(z)$, we say the filter bank is paraunitary.