Outline

In this chapter, we will look at a variety of ways to digitize macroscopic point-to-point transfer functions corresponding to a desired impulse response :

1. Sampling to get
2. Pole mappings (such as followed by Prony's method)
3. Modal expansion
4. Frequency-response matching using digital filter design methods

Next, we'll look at the more specialized technique known as commuted synthesis, in which computational efficiency may be greatly increased by interchanging (``commuting'') the series order of component transfer functions. Commuted synthesis delivers large gains in efficiency for systems with a short excitation and high-order resonators, such plucked and struck strings. In Chapter 9, commuted synthesis is applied to piano modeling.

Extracting the least-damped modes of a transfer function for separate parametric implementation is often used in commuted synthesis. We look at a number of ways to accomplish this goal toward the end of this chapter.

We close the chapter with a simple example of transfer-function modeling applied to the digital phase shifter audio effect. This example classifies as virtual analog modeling, in which a valued analog device is converted to digital form in a way that preserves all valued features of the original. Further examples of transfer-function models appear in Chapter 9.

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Next: Sampling the Impulse Response

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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.