Numerical Sound Synthesis

Transcription

1 Numerical Sound Synthesis Finite Difference Schemes and Simulation in Musical Acoustics Stefan Bilbao Acoustics and Fluid Dynamics Group/Music, University 01 Edinburgh, A John Wiley and Sons, Ltd., Publication

2 Contents Preface ix Sound synthesis and physical modeling I 1.1 Abstract digital sound synthesis Physical modeling Physical modeling: a larger view 18 2 Time series and difference operators Time series Shift, difference, and averaging operators Frequency domain analysis Energetic manipulations and identities Problems 42 3 The oscillator The simple harmonie oscillator A finite difference scheme Other schemes Lumped mass-spring networks Loss Sources Problems Programming exercises 71 4 The oscillator in musical acoustics Nonlinear oscillators Lossless oscillators Lossy oscillators Problems Programming exercises 90

3 vi 5 Grid functions and finite difference operators in 1D Partial differential operators and PDEs Grid functions and difference operators Coordinate changes Problems Programming exercises The I D wave equation Definition and properties A simple finite difference scheme Other schemes Modal synthesis Loss Comparative study I Problems Programming exercises Linear bar and string vibration The ideal uniform bar StifI strings Frequency-dependent loss Coupling with bow models Coupling with hammer and mallet models Multiple strings Prepared strings Coupled bars Helical springs Spatial variation and stretched coordinates Problems Programming exercises Nonlinear string vibration The Kirchhoff-Carrier string model General p1anar nonlinear string motion Non-planar string motion Problems Programming exercises Acoustic tubes Webster's equation The vocal tract and speech synthesis Reed wind instruments Other wind instruments Problems Programming exercises 283

4 vii 10 Grid functions and finite difference operators in 2D 10.1 Partial differential operators and PDEs in two space variables 10.2 Grid functions and difference operators: Cartesian coordinates 10.3 Grid functions and difference operators: radial coordinates 10.4 Problems 10.5 Programming exercises 11 The 2D wave equation 11.1 Definition and properties 11.2 A simple finite difference scheme 11.3 Other finite difference schemes 11.4 Digital waveguide meshes 11.5 Lumped mass-spring networks 11.6 Modal synthesis 11.7 Finite difference schemes in radial coordinates 11.8 Comparative study II 11.9 Problems Programming exercises 12 Linear plate vibration 12.1 The Kirchhoff thin plate model 12.2 Loss and tension 12.3 Plate excitation 12.4 Plate-string connections 12.5 Anisotropie plates 12.6 The thin plate in radial coordinates 12.7 Problems 12.8 Programming exercises 13 Nonlinear plate vibration 13.1 The Berger plate model 13.2 The von Karman plate model 13.3 Spherical shell vibration 13.4 Problems 13.5 Programming exercises 14 Conclusion and perspectives 14.1 A family of musical systems 14.2 Comparative study III 14.3 Beyond finite difference methods A Matlab code examples A.I The simple harmonie oscillator A.2 Hammer collision with mass-spring system A.3 Bowed mass-spring system

5 viii B AA The ID wave equation: finite difference scheme A.5 The ID wave equation: digital waveguidc synthesis A.6 The ID wave equation: modal synthesis A.7 The ideal bar A.8 The stiff string A.9 The Kirchhoff-Carrier equation A.lO Vocal synthesis A.l1 The 2D wave equation A.12 Thinplate List of symbols Bibliography Index