|Field of activity:||Multidimensional Signals and Systems Theory|
|Research topic:||Sound synthesis and sound field rendering|
|Staff:||Prof. Dr.-Ing. habil. Rudolf Rabenstein
M.Sc. Maximilian Schäfer
Many sound synthesis methods like sampling, frequency modulation (FM) synthesis, additive and subtractive synthesis model waveforms. This is good for creating new sounds, but it has several disadvantages in reproducing sounds of real acoustic instruments. The most important disadvantage is that the musician does not have the physically based variability of real musicalinstruments. Because of these disadvantages there are various methods for sound synthesis based on physical models that do not model the waveform but the sound production mechanism. They all start from from physical models in form of partial differential equations (PDEs), which can be obtained by applying the first principles of physics. But due to the differential operators the resulting PDEs can not be solved analytically.
The simplest approach to solve PDEs in the computer is the finite difference method. It discretizes the PDEs by writing the temporal and spatial derivatives as difference functions. Then the PDEs are replaced by finite difference equations that can easily be implemented in a computer. Drawbacks of this method are stability problems due to the discretization and the high computational complexity. The most common physical modeling method is the digital waveguide method (DWG). It simplifies the more complex PDE to the wave equation that can be solved analytically with the d'Alembert solution. This solution can be efficiently implemented by delay lines. To approximate the terms of the PDE neglected with the d'Alembert solution, transfer functions of low orders are included into the delay lines.
The method we are working on is based on multidimensional transfer function models. It can solve the various models given by different PDEs exactly. These solutions are then discretized and can be implemented in a computer. This discretization does not cause stability problems and preserves the natural frequencies of the oscillating body. Also the physical parameters can be varied directly with this method and therefore allow an intuitive way of playing.
As topic of their thesis work, numerous students have created so-called plugins for various audio platforms. Some of them are available for download on the following web pages.
LV2-Plugin "lv2_guitar" by Dipl. Ing. Andreas Kusterer
Csound-Plugin "tubesim" by Dipl. Ing. Marco Fink
VST-Plugin "FTM-Tube" by Dipl. Ing. Christian Popp and Dipl. Ing. Tilman Koch
VST-Plugin "AmpDelayWah" by Maximilian Schaefer
||M. Schäfer, P. Frenstátský, R. Rabenstein
A Physical String Model with Adjustable Boundary Conditions
19th International Conference on Digital Audio Effects (DAFx-16), Pages: 159 - 166, Brno, Czech Republic, Sep. 2016
Soliton Sonification - Experiments with the Korteweg-De Vries Equation
15th International Conference on Digital Audio Effects (DAFx), Pages: 71-78, York, UK, Sep. 2012
||Marco Fink, R. Rabenstein
A Csound Opcode for a Triode Stage of a Vacuum Tube Amplifier
International Conference on Digital Audio Effects (DAFx), Pages: 365-370, Paris, France, Sep. 2011
Spatial Sound Synthesis for Circular Membranes
13th International Conference on Digital Audio Effects (DAFx-10), Pages: 119-116, Graz, Austria, Sep. 2010
||R. Rabenstein, T. Koch, C. Popp
Tubular Bells: A Physical and Algorithmic Model
IEEE Transactions on Audio, Speech and Language Processing (IEEE TASLP) Vol. 18, Num. 4, Pages: 881-890, 2010