Digital Filter Models of Damped Strings

In an efficient digital simulation, lumped loss factors of the form are approximated by a rational frequency response . In general, the coefficients of the optimal rational loss filter are obtained by minimizing with respect to the filter coefficients or the poles and zeros of the filter. To avoid introducing frequency-dependent delay, the loss filter should be a zero-phase, finite-impulse-response (FIR) filter [371]. Restriction to zero phase requires the impulse response to be finite in length (i.e., an FIR filter) and it must be symmetric about time zero, i.e., . In most implementations, the zero-phase FIR filter can be converted into a causal, linear phase filter by reducing an adjacent delay line by half of the impulse-response duration.

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Order a Hardcopy of Physical Audio Signal Processing

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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.