Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

Properties of Paraunitary Filter Banks

An $ N$ -channel filter bank can be viewed as an $ N\times 1$ MIMO filter

$\displaystyle \mathbf{H}(z) = \left[\begin{array}{c} H_1(z) \\ [2pt] H_2(z) \\ [2pt] \vdots \\ [2pt] H_N(z)\end{array}\right]
$

A paraunitary filter bank must therefore obey

$\displaystyle {\tilde{\mathbf{H}}}(z)\mathbf{H}(z) = 1
$

More generally, we allow paraunitary filter banks to scale and/or delay the input signal [98]:

$\displaystyle {\tilde{\mathbf{H}}}(z)\mathbf{H}(z) = c_K z^{-K}
$

where $ K$ is some nonnegative integer and $ c_K\neq 0$ .

We can note the following properties of paraunitary filter banks:


Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

[How to cite this work]  [Order a printed hardcopy]  [Comment on this page via email]

``Introduction to Digital Filters with Audio Applications'', by Julius O. Smith III, (September 2007 Edition)
Copyright © 2024-09-03 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA