| Résumé |
Many audio systems and physical problems make some distortion appear as soon as the sound level increases. In this case, tools of linear signal processing are no longer suitable. A Volterra series is an input-to-output representation which is adapted to dynamical systems including some analytic nonlinearities. It extends notions of linear filtering: the “impulse response” and the “transfer function” are generalized into multi-variate “convolution kernels” and “transfer kernels”, respectively. These kernels isolate and sort the linear, quadratic, cubic (etc) homogeneous contributions of the dynamics. In this tutorial, Volterra series, their basic properties and their links with standard linear tools are presented. A practical method to solve nonlinear differential problems by using Volterra series is proposed in two steps. It sequentially answers to the following questions: (1) How to derive the transfer kernels for a given problem ? (2) How to build a realization and a simulation from the transfer kernels ? Then, applications on audio and acoustical problems are presented. Finally, some computable results on convergence domains and guaranteed error bounds are given. |
