Digital Sound Synthesis by Physical Modeling Using the Functional Transformation Method

By: Lutz Trautmann, Rudolf Rabenstein

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Hardcover | 31 October 2003

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256 Pages

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23.5 x 15.88 x 1.91

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This book considers signal processing and physical modeling meth ods for sound synthesis. Such methods are useful for example in mu sic synthesizers, computer sound cards, and computer games. Physical modeling synthesis has been commercialized for the first time about 10 years ago. Recently, it has been one of the most active research topics in musical acoustics and computer music. The authors of this book, Dr. Lutz Trautmann and Dr. Rudolf Rabenstein, are active researchers and inventors in the field of sound synthesis. Together they have developed a new synthesis technique, called the functional transformation method, which can be used for pro ducing musical sound in real time. Before this book, they have published over 20 papers on the topic in journals and conference proceedings. In this excellent textbook, the results are combined in a single volume. I believe that this will be considered an important step forward for the whole community.

Industry Reviews

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)

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Introduction	p. 1
Sound-Based Synthesis Methods	p. 5
Wavetable synthesis	p. 5
Looping	p. 6
Pitch shifting	p. 6
Enveloping	p. 7
Filtering	p. 7
Granular synthesis	p. 8
Asynchronous granular synthesis	p. 8
Pitch-synchronous granular synthesis	p. 9
Additive synthesis	p. 10
Subtractive synthesis	p. 11
FM synthesis	p. 11
Combinations of sound-based synthesis methods	p. 12
Physical Description of Musical Instruments	p. 15
General notation	p. 16
Subdivision of a musical instrument into vibration generators and a resonant body	p. 19
Division of stringed instruments into single strings and the resonant body	p. 19
Construction of stringed instruments	p. 19
Fixed strings filtered with the resonant body	p. 21
Strings terminated with independent impedances	p. 22
Strings terminated with an impedance network	p. 24
Division of a kettle drum into a membrane and the kettle	p. 25
Construction of drums	p. 26
Drum body simulation by modifying the physical parameters of the membrane	p. 27
Drum body simulation by room acoustic simulation with the membrane as vibrating boundary	p. 27
Physical description of string vibrations	p. 27
Longitudinal string vibrations	p. 29
Torsional string vibrations	p. 35
Transversal string vibrations	p. 40
Basic linear model	p. 40
Nonlinear excitation functions	p. 47
Nonlinear PDE with solution-dependent coefficients	p. 51
Physical description of membrane vibrations	p. 52
Bending membrane vibrations	p. 52
Physical description of resonant bodies	p. 57
Chapter summary	p. 60
Classical Synthesis Methods Based on Physical Models	p. 63
Finite difference method	p. 64
FDM applied to scalar PDEs	p. 68
FDM applied to vector PDEs	p. 73
Digital waveguide method	p. 76
Digital waveguides simulating string vibrations	p. 77
Digital waveguide meshes simulating membrane vibrations	p. 83
Modal synthesis	p. 86
Chapter summary	p. 92
Functional Transformation Method	p. 95
Fundamental principles of the FTM	p. 96
FTM applied to scalar PDEs	p. 100
Laplace transformation	p. 101
Sturm-Liouville transformation	p. 102
Transfer function model	p. 110
Discretization of the MD TFM	p. 112
Inverse Sturm-Liouville transformation	p. 114
Inverse z-transformation	p. 116
FTM applied to vector PDEs	p. 118
Laplace transformation	p. 119
Sturm-Liouville transformation	p. 120
Transfer function model	p. 126
Discretization of the MD TFM	p. 127
Inverse Sturm-Liouville transformation	p. 128
Inverse z-transformation	p. 128
FTM applied to PDEs with nonlinear excitation functions	p. 130
FTM applied to PDEs with solution-dependent coefficients	p. 137
Stability and simulation accuracy of the FTM	p. 143
Section summary	p. 145
Application of the FTM to vibrating strings	p. 145
Transversal string vibrations described by a scalar PDE	p. 146
Longitudinal string vibrations described by vector PDEs	p. 151
Boundary conditions of second kind	p. 152
Boundary conditions of third kind	p. 155
Two interconnected strings	p. 159
Transversal string vibrations with nonlinear excitation functions	p. 163
Piano hammer excitation	p. 164
Slapped bass	p. 167
Transversal string vibrations with tension-modulated nonlinearities	p. 170
Application of the FTM to vibrating membranes	p. 175
Rectangular reverberation plate	p. 176
Circular drum heads	p. 178
Application of the FTM to resonant bodies	p. 182
Chapter summary	p. 186
Comparison of the FTM with the Classical Physical Modeling Methods	p. 189
Comparison of the FTM with the FDM	p. 190
Comparison and combination of the FTM with the DWG	p. 196
Comparison of the FTM with the DWG	p. 196
Combination of the DWG with the FTM	p. 200
Designing the loss filter	p. 201
Designing the dispersion filter	p. 203
Designing the fractional delay filter	p. 205
Adjusting the excitation function	p. 205
Limits of the combination	p. 206
Comparison of the FTM with the MS	p. 208
Chapter conclusions	p. 210
Summary, Conclusions, and Outlook	p. 213
Index	p. 225
Table of Contents provided by Rittenhouse. All Rights Reserved.

Digital Sound Synthesis by Physical Modeling Using the Functional Transformation Method

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Hardcover

Industry Reviews

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