Báo cáo hóa học: " Research Article Analysis of Damped Mass-Spring Systems for Sound Synthesis"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Analysis of Damped Mass-Spring Systems for Sound Synthesis | Hindawi Publishing Corporation EURASIP Journal on Audio Speech and Music Processing Volume 2009 Article ID 947823 19 pages doi 2009 947823 Research Article Analysis of Damped Mass-Spring Systems for Sound Synthesis Don Morgan and Sanzheng Qiao Department of Computing and Software McMaster University Hamilton ON Canada L8S 4L7 Correspondence should be addressed to Don Morgan mordon700@ Received 26 July 2008 Revised 1 December 2008 Accepted 20 February 2009 Recommended by Thippur Sreenivas 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 massspring 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. Copyright 2009 D. Morgan and S. Qiao. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction Physical sound synthesis uses mathematical models based on the physics of sound production to synthesize sound. In other words physical sound synthesis uses a model to simulate the sound producing object rather than the sound produced by an object. In this paper we focus on massspring systems networks of masses springs and dampers. The mathematical model of mass-spring systems is based

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