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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2009-01-01
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Series: | EURASIP Journal on Audio, Speech, and Music Processing |
Online Access: | http://dx.doi.org/10.1155/2009/947823 |
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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 |
_version_ |
1725106246711771136 |