Analysis of Damped Mass-Spring Systems for Sound Synthesis

There are many ways of synthesizing sound on a computer. The method that we consider, called a mass-spring system, synthesizes sound by simulating the vibrations of a network of interconnected masses, springs, and dampers. Numerical methods are required to approximate the differential equation of a...

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Main Authors: Don Morgan, Sanzheng Qiao
Format: Article
Language:English
Published: SpringerOpen 2009-01-01
Series:EURASIP Journal on Audio, Speech, and Music Processing
Online Access:http://dx.doi.org/10.1155/2009/947823
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spelling doaj-2b1a2678253246c59b040ad4fc40d9032020-11-25T01:27:13ZengSpringerOpenEURASIP Journal on Audio, Speech, and Music Processing1687-47141687-47222009-01-01200910.1155/2009/947823Analysis of Damped Mass-Spring Systems for Sound SynthesisDon MorganSanzheng QiaoThere are many ways of synthesizing sound on a computer. The method that we consider, called a mass-spring system, synthesizes sound by simulating the vibrations of a network of interconnected masses, springs, and dampers. Numerical methods are required to approximate the differential equation of a mass-spring system. The standard numerical method used in implementing mass-spring systems for use in sound synthesis is the symplectic Euler method. Implementers and users of mass-spring systems should be aware of the limitations of the numerical methods used; in particular we are interested in the stability and accuracy of the numerical methods used. We present an analysis of the symplectic Euler method that shows the conditions under which the method is stable and the accuracy of the decay rates and frequencies of the sounds produced. http://dx.doi.org/10.1155/2009/947823
collection DOAJ
language English
format Article
sources DOAJ
author Don Morgan
Sanzheng Qiao
spellingShingle Don Morgan
Sanzheng Qiao
Analysis of Damped Mass-Spring Systems for Sound Synthesis
EURASIP Journal on Audio, Speech, and Music Processing
author_facet Don Morgan
Sanzheng Qiao
author_sort Don Morgan
title Analysis of Damped Mass-Spring Systems for Sound Synthesis
title_short Analysis of Damped Mass-Spring Systems for Sound Synthesis
title_full Analysis of Damped Mass-Spring Systems for Sound Synthesis
title_fullStr Analysis of Damped Mass-Spring Systems for Sound Synthesis
title_full_unstemmed Analysis of Damped Mass-Spring Systems for Sound Synthesis
title_sort analysis of damped mass-spring systems for sound synthesis
publisher SpringerOpen
series EURASIP Journal on Audio, Speech, and Music Processing
issn 1687-4714
1687-4722
publishDate 2009-01-01
description There are many ways of synthesizing sound on a computer. The method that we consider, called a mass-spring system, synthesizes sound by simulating the vibrations of a network of interconnected masses, springs, and dampers. Numerical methods are required to approximate the differential equation of a mass-spring system. The standard numerical method used in implementing mass-spring systems for use in sound synthesis is the symplectic Euler method. Implementers and users of mass-spring systems should be aware of the limitations of the numerical methods used; in particular we are interested in the stability and accuracy of the numerical methods used. We present an analysis of the symplectic Euler method that shows the conditions under which the method is stable and the accuracy of the decay rates and frequencies of the sounds produced.
url http://dx.doi.org/10.1155/2009/947823
work_keys_str_mv AT donmorgan analysisofdampedmassspringsystemsforsoundsynthesis
AT sanzhengqiao analysisofdampedmassspringsystemsforsoundsynthesis
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