Digital Sound Synthsis using Physical Modeling
Many sound synthesis methods like sampling, frequency modulation (FM) synthesis, additive and subtractive synthesis model sound. This is good for creating new sounds, but has several disadvantages in reproducing sounds of real acoustic instruments. The most important disadvantage is that the musician does not have the physical based variability he has with real musicalinstruments. Therefore it is difficult to phrase a melody with these methods.
Because of these disadvantages there are various methods for sound synthesis based on physical models that do not model the sound but the sound production mechanism. They all start from from physical models in form of partial differential equations (PDEs). They 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 widespread 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 big advantage of the DWG is the low computational complexity, but there are also several disadvantages. One of them is the non-physical based control of the transfer function coefficients.
The method we are working on is based on multidimensional transfer function models. It can solve the various models given by different PDEs exactely. 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.
Current research
As already mentioned, the sound synthesis group in the laboratory focusses on the functional transformation method (FTM) for the realistic and intuitive sound synthesis of musical instruments. Several instruments are yet implemented, mainly string instruments like guitars, pianos and violins, but even two-dimensional models like drums.
For more details on them see:
Recently we are working on the EU shared cost project ALMA (ALgorithms for the Modelling of Acoustic interactions), which tries to combine and unify all sound synthesis methods, especially physical modelling methods, as they are described above. The goal of the project is to develop an elegant, general and unifying strategy for a block-wise design of nonlinear physical and pseudo-physical models in sound synthesis.
Demos
Several sound demos are available:
Electric bass guitar,
Slapped bass guitar,
transformation from a guitar string to a xylophone,
lowest piano note,
polyphonial spinet,
Kettle drum,
Tom high,
Tom low,
metal drum high,
metal drum low
A VST-plugin for real-time sound synthesis of string instruments can be
downloaded for free:
VST-Plugin "FTM String"
Two Windows-program for the visualization and sonification of circular and recangular membranes are available:
Wave2D and membsim
Our algorithms are even implemented in professional, commercial sound hardware:
Six-String Plugin from CreamWare
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