| Volterra filters are a popular choice for modelling many nonlinear systems, in part due to their generality and simplicity in implementation and adaptation. This thesis addresses one often cited problem with this class of filters: the large increase in the number of terms in the filter for small increases in order or memory. Adaptive algorithms are presented which allow much smaller filters to perform near the performance (in terms of residual error) of the full Volterra filters. The complexity is maintained at reasonable levels by only representing the terms that are critical in reducing the error. An alternative representation with real valued exponents is introduced from the Volterra series representation, and is used to determine the optimum nonlinear filter (in the mean squared error sense) from this class of filters. Examples verifying the performance of the proposed algorithms are presented. These algorithms allow the design of models of much higher order than currently used for such problems as loudspeaker equalization, image processing, and noise removal, among others. |
