Transfer Function Models

As indicated in the previous section, instead of digitizing a differential equation by finite differences, one can often formulate a filter design problem. This is ideal when all that matters is the input-output response of the physical system, and the physical system is linear and time-invariant (LTI). When the desired transfer function spans more than one system element, non-physical models are usually obtained, so we will not consider such models further. However, digital filter design methods optimizing perceptually motivated error criteria are extremely effective in spectral modeling and audio compression applications [337]. They are also good choices for subsystems which are to remain fixed over time, such as cello bodies, piano soundboards, and the like.

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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.