Digital Sound Synthesis by Physical Modeling Using the Functional Transformation Method
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Digital Sound Synthesis by Physical Modeling Using the Functional Transformation Method

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Rudolf Rabenstein
392 g
235x155x13 mm

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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 Drum body 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 Sturm-Liouville transformation.- 1.1.3 Transfer function model.- 1.1.4 Discretization of the MD TFM.- 1.1.5 Inverse Sturm-Liouville transformation.- 1.1.6 Inverse z-transformation.- 1.2 FTM applied to vector PDEs.- 1.2.1 Laplace transformation.- 1.2.2 Sturm-Liouville transformation.- 1.2.3 Transfer function model.- 1.2.4 Discretization of the MD TFM.- 1.2.5 Inverse Sturm-Liouville transformation.- 1.2.6 Inverse z-transformation.- 1.3 FTM applied to PDEs with nonlinear excitation functions.- 1.4 FTM applied to PDEs with solution-dependent coefficients.- 1.5 Stability and simulation accuracy of the FTM.- 1.6 Section summary.- 2 Application of the FTM to vibrating strings.- 2.1 Transversal string vibrations described by a scalar PDE.- 2.2 Longitudinal string vibrations described by vector PDEs.- 2.2.1 Boundary conditions of second kind.- 2.2.2 Boundary conditions of third kind.- 2.2.3 Two interconnected strings.- 2.3 Transversal string vibrations with nonlinear excitation functions.- 2.3.1 Piano hammer excitation.- 2.3.2 Slapped bass.- 2.4 Transversal string vibrations with tension-modulated nonlinearities.- 3 Application of the FTM to vibrating membranes.- 3.1 Rectangular reverberation plate.- 3.2 Circular drum heads.- 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.- 2.1 Comparison of the FTM with the DWG.- 2.2 Combination of the DWG with the FTM.- 2.2.1 Designing the loss filter.- 2.2.2 Designing the dispersion filter.- 2.2.3 Designing the fractional delay filter.- 2.2.4 Adjusting the excitation function.- 2.3 Limits of the combination.- 3 Comparison of the FTM with the MS.- 4 Chapter conclusions.- 7. Summary, Conclusions, and Outlook.
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.

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