A Musical Time-Varying Filter Example

Note, however, that a gain may vary with time independently of to yield a linear time-varying filter. In this case, linearity may be demonstrated by verifying

to show that both scaling and superposition hold. A simple example of a linear time-varying filter is a tremolo function, which can be written as a time-varying gain, . For example, would give a maximally deep tremolo with 4 swells per second.

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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.