Paraunitary Filter Banks

Paraunitary filter banks form an interesting subset of perfect reconstruction (PR) filter banks. We saw above that we get a PR filter bank whenever the synthesis polyphase matrix times the analysis polyphase matrix is the identity matrix , i.e., when

In particular, if is the paraconjugate of , we say the filter bank is paraunitary.

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Subsections

• Paraconjugation
• Lossless Filters
• Lossless Filter Examples
• Properties of Paraunitary Systems
• Properties of Paraunitary Filter Banks
• Paraunitary Examples

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Order a Hardcopy of Spectral Audio Signal Processing

Previous: Example: Polyphase Analysis of the Weighted Overlap Add Case: 50% Overlap, Zero-Padding, and a Non-Rectangular Window
Next: Paraconjugation

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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.