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


FFT Spectral Analysis 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?


Finite-Difference Schemes

This appendix gives some simplified definitions and results from the subject of finite-difference schemes for numerically solving partial differential equations. Excellent references on this subject include Bilbao [53,55] and Strikwerda [481].

The simplifications adopted here are that we will exclude nonlinear and time-varying partial differential equations (PDEs). We will furthermore assume constant step-sizes (sampling intervals) when converting PDEs to finite-difference schemes (FDSs), i.e., sampling rates along time and space will be constant. Accordingly, we will assume that all initial conditions are bandlimited to less than half the spatial sampling rate, and that all excitations over time (such as summing input signals or ``moving boundary conditions'') will be bandlimited to less than half the temporal sampling rate. In short, the simplifications adopted here make the subject of partial differential equations isomorphic to that of linear systems theory [449]. For a more general and traditional treatment of PDEs and their associated finite-difference schemes, see, e.g., [481].

Previous: Poles at
Next: Finite-Difference Schemes

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? )