Numerical sound synthesis : finite difference schemes and simulation in musical acoustics / Stefan Bilbao.

Format:

Book

Author/Creator:

Bilbao, Stefan D.

Language:

English

Subjects (All):

Musical instruments--Mathematical models.

Musical instruments.

Musical instruments--Computer simulation.

Finite differences.

Physical Description:

1 online resource (457 p.)

Edition:

1st ed.

Place of Publication:

[Hoboken] : John Wiley & Sons, 2009.

Language Note:

English

Summary:

Digital sound synthesis has long been approached using standard digital filtering techniques. Newer synthesis strategies, however, make use of physical descriptions of musical instruments, and allow for much more realistic and complex sound production and thereby synthesis becomes a problem of simulation. This book has a special focus on time domain finite difference methods presented within an audio framework. It covers time series and difference operators, and basic tools for the construction and analysis of finite difference schemes, including frequency-domain and energy-based methods, wi

Contents:

Numerical Sound Synthesis; Contents; Preface; 1 Sound synthesis and physical modeling; 1.1 Abstract digital sound synthesis; 1.2 Physical modeling; 1.3 Physical modeling: a larger view; 2 Time series and difference operators; 2.1 Time series; 2.2 Shift, difference, and averaging operators; 2.3 Frequency domain analysis; 2.4 Energetic manipulations and identities; 2.5 Problems; 3 The oscillator; 3.1 The simple harmonic oscillator; 3.2 A finite difference scheme; 3.3 Other schemes; 3.4 Lumped mass-spring networks; 3.5 Loss; 3.6 Sources; 3.7 Problems; 3.8 Programming exercises

4 The oscillator in musical acoustics4.1 Nonlinear oscillators; 4.2 Lossless oscillators; 4.3 Lossy oscillators; 4.4 Problems; 4.5 Programming exercises; 5 Grid functions and finite difference operators in 1D; 5.1 Partial differential operators and PDEs; 5.2 Grid functions and difference operators; 5.3 Coordinate changes; 5.4 Problems; 5.5 Programming exercises; 6 The 1D wave equation; 6.1 Definition and properties; 6.2 A simple finite difference scheme; 6.3 Other schemes; 6.4 Modal synthesis; 6.5 Loss; 6.6 Comparative study I; 6.7 Problems; 6.8 Programming exercises

7 Linear bar and string vibration7.1 The ideal uniform bar; 7.2 Stiff strings; 7.3 Frequency-dependent loss; 7.4 Coupling with bow models; 7.5 Coupling with hammer and mallet models; 7.6 Multiple strings; 7.7 Prepared strings; 7.8 Coupled bars; 7.9 Helical springs; 7.10 Spatial variation and stretched coordinates; 7.11 Problems; 7.12 Programming exercises; 8 Nonlinear string vibration; 8.1 The Kirchhoff-Carrier string model; 8.2 General planar nonlinear string motion; 8.3 Non-planar string motion; 8.4 Problems; 8.5 Programming exercises; 9 Acoustic tubes; 9.1 Webster's equation

9.2 The vocal tract and speech synthesis9.3 Reed wind instruments; 9.4 Other wind instruments; 9.5 Problems; 9.6 Programming exercises; 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 meshes11.5 Lumped mass-spring networks; 11.6 Modal synthesis; 11.7 Finite difference schemes in radial coordinates; 11.8 Comparative study II; 11.9 Problems; 11.10 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 Anisotropic 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 K ́arm ́an plate model; 13.3 Spherical shell vibration

13.4 Problems

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786612291715

9781282291713

1282291718

9780470749012

0470749016

9780470749029

0470749024

OCLC:

609849315