Digital Sound Synthesis by Physical Modeling Using the Functional Transformation Method - Lutz Trautmann

. .

Résumé :
This book derives and discusses the current state of the art in physical modelling 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 finite difference method, digital waveguide method, and modal synthesis method. The focus of this book is on the new functional transformation method, providing an analytical solution to the underlying mathematical model. BRWith its large number of examples, illustrations and comparisons to other modelling 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.

Sommaire:
1. Introduction.- 2. Sound-Based Synthesis Methods.- 1 Wavetable synthesis.- 2 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.- 3 Physical description of string vibrations.- 4 Physical description of membrane vibrations.- 5 Physical description of resonant bodies.- 6 Chapter summary.- 4. Classical Synthesis Methods Based on Physical Models.- 1 Finite difference method.- 2 Digital waveguide method.- 3 Modal synthesis.- 4 Chapter summary.- 5. Functional Transformation Method.- 1 Fundamental principles of the FTM.- 2 Application of the FTM to vibrating strings.- 3 Application of the FTM to vibrating membranes.- 4 Application of the FTM to resonant bodies.- 5 Chapter summary.- 6. Comparison of the Ftm with the Classical Physical Modeling Methods.- 1 Comparison of the FTM with the FDM.- 2 Comparison and combination of the FTM with the DWG.- 3 Comparison of the FTM with the MS.- 4 Chapter conclusions.- 7. Summary, Conclusions, and Outlook.

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)