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The creation of synthetic sounds plays an increasing role in multimedia signal processing. A variety of methods already used in digital musical instruments are now applied for sound rendering of virtual scenes. Most of these methods rely on the description of waveforms in terms of harmonics, attack and decay times, etc. However, these parameters have to be measured in real sounds or they must be derived from suitable models. In practice, their choice is left to the taste of a sound designer and is not based on scientific methods. This paper shows how to apply the theory of multidimensional continuous and discrete systems to derive a parametric description of musical sounds from a physical model of real or virtual musical instruments. Furthermore, it is shown that not only the parameters but also the algorithmic structure of powerful sound synthesis methods can be derived from multidimensional systems theory.