Digital Sound Synthesis by Physical Modeling Using the Functional Transformation Method

1. Introduction.- 2. Sound-Based Synthesis Methods.- 1 Wavetable synthesis.- 1.1 Looping.- 1.2 Pitch shifting.- 1.3 Enveloping.- 1.4 Filtering.- 2 Granular synthesis.- 2.1 Asynchronous granular synthesis.- 2.2 Pitch-synchronous granular synthesis.- 3 Additive synthesis.- 4 Subtractive synthesis.- 5 FM synthesis.- 6 Combinations of sound-based synthesis methods.- 3. Physical Description of Musical instruments.- 1 General notation.- 2 Subdivision of a musical instrument into vibration generators and a resonant body.- 2.1 Division of stringed instruments into single strings and the resonant body.- 2.1.1 Construction of stringed instruments.- 2.1.2 Fixed strings filtered with the resonant body.- 2.1.3 Strings terminated with independent impedances.- 2.1.4 Strings terminated with an impedance network.- 2.2 Division of a kettle drum into a membrane and the kettle.- 2.2.1 Construction of drums.- 2.2.2 Drum body simulation by modifying the physical parameters of the membrane.- 2.2.3 Drumbody simulation by room acoustic simulation with the membrane as vibrating boundary.- 3 Physical description of string vibrations.- 3.1 Longitudinal string vibrations.- 3.2 Torsional string vibrations.- 3.3 Transversal string vibrations.- 3.3.1 Basic linear model.- 3.3.2 Nonlinear excitation functions.- 3.3.3 Nonlinear PDE with solution-dependent coefficients.- 4 Physical description of membrane vibrations.- 4.1 Bending membrane vibrations.- 5 Physical description of resonant bodies.- 6 Chapter summary.- 4. Classical Synthesis Methods Based on Physical Models.- 1 Finite difference method.- 1.1 FDM applied to scalar PDEs.- 1.2 FDM applied to vector PDEs.- 2 Digital waveguide method.- 2.1 Digital waveguides simulating string vibrations.- 2.2 Digital waveguide meshes simulating membrane vibrations.- 3 Modal synthesis.- 4 Chapter summary.- 5. Functional Transformation Method.- 1 Fundamental principles of the FTM.- 1.1 FTM applied to scalar PDEs.- 1.1.1 Laplace transformation.- 1.1.2

From the reviews: "This is a book devoted to digital sound synthesis (DSS). The exposition makes full use of modern mathematical tools. ! The book represents an interesting contribution to music synthesis and the reviewer thinks it will soon become a reference volume in the electric and mechanical domains." (D. Stanomir, Mathematical Reviews, 2005 b) "This book ! gives not only a thorough introduction to the Functional Transformation Method itself, but provides an excellent overview of existing alternatives. ! The book is exemplary in clarity as well as for references and lists of symbols, variables, abbreviations, etc. More than fifty figures are included. ! an innovative and far-reaching text that should find its way to all institutes where sound synthesis is taught or researched." (K. Guettler, Acta Acustica united with Acustica, Vol. 91 (4), 2005)