Book on Digital Sound Synthesis by Physical Modeling Using the Functional Transformation Method by Lutz Trautmann and Rudolf Rabenstein ISBN: 0-306-47875-7 Kluwer Academic Pubishers, 2003

Digital Sound Synthesis by Physical Modeling Using the Functional Transformation Method derives and discusses the current state of the art in physical modeling of musical instruments for real-time sound synthesis. It includes the derivation of mathematical models in the form of partial differential equations for the vibrational description of strings, membranes/plates, and resonant bodies. Their solution and simulation is first described by classical methods, including the finite difference method, digital waveguide method, and modal synthesis method. The focus of the text is on the new functional transformation method, providing an analytical solution to the underlying mathematical model. With its large number of examples, illustrations and comparisons to other modeling techniques, this book is an excellent reference for graduate courses on sound synthesis techniques, as well as a reference for researchers in acoustics, mechanics, operational mathematics, and electrical engineering.

Contents

1. Introduction
2. Sound-Based Synthesis Methods
3. Physical Description of Musical Instruments
4. Classical Synthesis Methods based on Physical Models
5. Functional Transformation Method
6. Comparison of the FTM with the Classical Physical Modeling Methods
7. Summary, Conclusions, and Outlook