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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:


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``Introduction to Digital Filters with Audio Applications'', by Julius O. Smith III, (September 2007 Edition).
Copyright © 2014-03-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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