Type II Polyphase Decomposition

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The preceding polyphase decomposition of into channels

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

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

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

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

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

written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.

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