Biorthogonal Signal Expansions

A set of signals is said to be a biorthogonal basis set if any signal can be represented as

where is some normalizing scalar dependent only on and/or . Thus, in a biorthogonal system, we project onto the signals and resynthesize in terms of .

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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.