Digital Sound Synthesis by Physical Modeling Using the Functional Transformation Method

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.