Digitizing Bridge Reflectance

Converting continuous-time transfer functions such as and to the digital domain is analogous to converting an analog electrical filter to a corresponding digital filter--a problem which has been well studied [343]. For this task, the bilinear transform (§7.3.2) is a good choice. In addition to preserving order and being free of aliasing, the bilinear transform preserves the positive-real property of passive impedances (§C.11.2).

Digitizing via the bilinear transform (§7.3.2) transform gives

which is a second-order digital filter having gain less than one at all frequencies--i.e., it is a Schur filter that becomes an allpass as the damping approaches zero. The choice of bilinear-transform constant maps the peak-frequency without error (see Problem 4).

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About the Author: 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.