Stability of a Finite-Difference Scheme

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Index: Physical Audio Signal Processing

Physical Audio Signal Processing

Convergence

Proof that the Third-Order Time Derivative is Ill Posed

Lax-Richtmyer equivalence theorem

A digital filter can be visualized as a 'black box' that accepts a sequence of numbers and emits a new sequence of numbers. In digital audio signal processing applications, such number sequences usually represent sounds. For example, digital filters are used to implement graphic equalizers and other digital audio effects. — Click for https://ccrma.stanford.edu/~jos/filters/

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A filter is said to be stable if its impulse response decays to zero as time goes to infinity — Click for https://ccrma.stanford.edu/~jos/filters/Stability_Revisited.html

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Index: Physical Audio Signal Processing

Physical Audio Signal Processing

Convergence

Proof that the Third-Order Time Derivative is Ill Posed

Lax-Richtmyer equivalence theorem

Stability of a Finite-Difference Scheme

A finite-difference scheme is said to be stable if it forms a digital filter which is at least marginally stable [452].

To distinguish between the stable and marginally stable cases, we may classify a finite-difference scheme as strictly stable, marginally stable, or unstable.

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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4
Copyright © 2024-06-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

Stability of a Finite-Difference Scheme

``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4 Copyright © 2024-06-28 by Julius O. Smith III Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4
Copyright © 2024-06-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University