This book deals with signal processing and physical methods for sound synthesis and contains 7 chapters. Chapter 1 serves as an introduction, and here a brief general and historical overview of the technical field of sound synthesis is given. The main sound-based synthesis methods such as wavetable, granular, adaptive, subtractive, frequency modulation synthesis and some of their combinations are described in chapter 2. A general mathematical description of musical instruments in the form of partial differential equations in both scalar and vector form subject to corresponding initial and boundary conditions are developed in chapter 3. A decomposition approach is used for investigating the proposed equations, i.e. musical instruments are divided into substructures like vibrating string (1-D), vibrating membranes (2-D) and resonant bodies (3-D). Subsequently, relations between the substructures are taken into account by linear and nonlinear interaction schemes. The computer implementations of these continuous mathematical models are considered in chapter 4.
The Functional Transfer Method (FTM) for digital sound synthesis is described in chapter 5. This method, based on the functional transformations with respect to time and space, is used to analytically solve the equations developed in previous chapters. Here, to check the validity of analytical solutions, the simulation approach is used. In chapter 6 a comparison of the FTM with the well-known classical physical modeling methods (i.e. finite difference method, the digital waveguide method and the model synthesis method) is given. Concluding remarks and future research directions for FTM are presented in chapter 7.