Sign in

Not a member? | Forgot your Password?

Search Online Books

Search tips

Free Online Books

Free PDF Downloads

A Quadrature Signals Tutorial: Complex, But Not Complicated

Understanding the 'Phasing Method' of Single Sideband Demodulation

Complex Digital Signal Processing in Telecommunications

Introduction to Sound Processing

C++ Tutorial

Introduction of C Programming for DSP Applications

Fixed-Point Arithmetic: An Introduction

Cascaded Integrator-Comb (CIC) Filter Introduction


IIR Filter Design Software

See Also

Embedded SystemsFPGA

Chapter Contents:

Search Physical Audio Signal Processing


Book Index | Global Index

Would you like to be notified by email when Julius Orion Smith III publishes a new entry into his blog?


Digital Waveguide Models

In this chapter, we summarize the basic principles of digital waveguide models. Such models are used for efficient synthesis of string and wind musical instruments (and tonal percussion, etc.), as well as for artificial reverberation. They can be further used in modal synthesis by efficiently implementing a quasi harmonic series of modes in a single ``filtered delay loop''.

We begin with the simplest case of the infinitely long ideal vibrating string, and the model is unified with that of acoustic tubes. The resulting computational model turns out to be a simple bidirectional delay line. Next we consider what happens when a finite length of ideal string (or acoustic tube) is rigidly terminated on both ends, obtaining a delay-line loop. The delay-line loop provides a basic digital-waveguide synthesis model for (highly idealized) stringed and wind musical instruments. Next we study the simplest possible excitation for a digital waveguide string model, which is to move one of its (otherwise rigid) terminations. Excitation from ``initial conditions'' is then discussed, including the ideal plucked and struck string. Next we introduce damping into the digital waveguide, which is necessary to model realistic losses during vibration. This much modeling yields musically useful results. Another linear phenomenon we need to model, especially for piano strings, is dispersion, so that is taken up next. Following that, we consider general excitation of a string or tube model at any point along its length. Methods for calibrating models from recorded data are outlined, followed by modeling of coupled waveguides, and simple memoryless nonlinearities are introduced and analyzed.

Previous: Recent Research Modeling the Leslie
Next: Ideal Vibrating String

Order a Hardcopy of Physical Audio Signal Processing

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 (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 for details.


No comments yet for this page

Add a Comment
You need to login before you can post a comment (best way to prevent spam). ( Not a member? )