nonlinear dynamical system
state space reconstruction
In this article a new approach for modeling sound is described, which is based on the method of dynamic modeling. This approach has been developed to model nonlinear dynamical systems given only a time series of samples that has been measured from the output of the system. The basic idea of the method emerged when it has been discovered that rather simple nonlinear systems can produce complex signals and that the state space of a system can be reconstructed given only an output signal of the system. While dynamic modeling has been originally intended to model chaotic dynamics the approach can be applied in the general case of non chaotic dynamics, also. This establishes the possibility to model sound dynamics based on dynamic modeling. A major goal for dynamic modeling is to find a model that can reproduce the systems dynamics. Because the state space reconstruction establishes a link between signal and state space evolution the model can be used to resynthesize sounds that differ on a sample by sample basis, however, follow the same dynamics.
Article paru dans : Computer Music Journal vol. 25 n°2