Modélisation non linéaire de la chaîne instrumentale pour guitare permettant son émulation en temps réel

Nonlinear systems identification and modeling is a central topic in many engineering areas since most real world devices may exhibit a nonlinear behavior. This thesis is devoted to the emulation of the nonlinear devices present in a guitar signal chain. The emulation aims to replace the hardware elements of the guitar signal chain in order to reduce its cost, its size, its weight and to increase its versatility. The challenge consists in enabling an accurate nonlinear emulation of the guitar signal chain while keeping the execution time of the model under the real time constraint. To do so, we have developed two methods. The first method developed in this thesis is based on a subclass of the Volterra series where only static nonlinearities are considered: the polynomial parallel cascade of Hammerstein models. The resulting method is called the Hammerstein Kernels Identification by Sine Sweep method (HKISS). According to the tests carried out in this thesis and to the results obtained, the method enables an accurate emulation of nonlinear audio devices unless if the system to model is too far from an ideal Hammerstein one. The second method, based on neural networks, better generalizes to guitar signals and is well adapted to the emulation of guitar signal chain (e.g., tube and transistor amplifiers). We developed and compared eight models using different performance indexes including listening tests. The accuracy obtained depends on the tested audio device and on the selected model but we have shown that the probability for a listener to be able to hear a difference between the target and the prediction could be less than 1%. This method could still be improved by training the neural networks with an objective function that better corresponds to the objective of this audio application, i.e., minimizing the audible difference between the target and the prediction. Finally, it is shown that these two methods enable an accurate emulation of a guitar signal chain while keeping a fast execution time which is required for real-time audio applications