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Polyphase Decomposition

The previous section derived an efficient polyphase implementation of an FIR filter $ h$ whose output was downsampled by the factor $ N$ . The derivation was based on commuting the downsampler with the FIR summer. We now derive the polyphase representation of a filter of any length algebraically by splitting the impulse response $ h$ into $ N$ polyphase components.



Subsections
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``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2022-02-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA