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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:

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


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``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2016-07-18 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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