Chair of
Multimedia Communications and Signal Processing
Prof. Dr.-Ing. André Kaup
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# Sound synthesis

Field of activity: Multidimensional Signals and Systems Theory Sound synthesis and sound field rendering Prof. Dr.-Ing. habil. Rudolf RabensteinM.Sc. Maximilian Schäfer

## Description

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

Solitonen-Sonification

## Publications

 2016-25CRIS 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
 2012-49CRIS R. Rabenstein Soliton Sonification - Experiments with the Korteweg-De Vries Equation 15th International Conference on Digital Audio Effects (DAFx), Pages: 71-78, York, UK, Sep. 2012
 2011-54CRIS 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
 2010-39CRIS R. Rabenstein Spatial Sound Synthesis for Circular Membranes 13th International Conference on Digital Audio Effects (DAFx-10), Pages: 119-116, Graz, Austria, Sep. 2010
 2010-37CRIS 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