Bilinear Transformation

The bilinear transform may be defined by

where is an arbitrary positive constant that we may set to map one analog frequency precisely to one digital frequency. In the case of a lowpass or highpass filter, is typically used to set the cut-off frequency to be identical in the analog and digital cases.

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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.