Application of Fast Wavelet Transformation in Parametric System Identification

Abstract

This work deals with discrete embedding of system operators in identification models on basis of Fast Wavelet Transformation (FWT). In particular for FWT-models of linear dynamic systems the missing variables can be calculated with the help of connection coefficients. The application of connection coefficients provides the direct projection of the system operators into the corresponding wavelet space. Here a class of operators is introduced, which satisfies certain permutability relations with respect to dilations and translations. This class contains especially derivation and integration operators and some special convolution operators, like the Hilbert-transform. Such a definition allows the systematic determination of generalized connection coefficients. It gives so the possibility to realize identification procedures for different models and their implementations in a unified pattern. The method can be used for all biorthogonal wavelet systems whose synthesis functions are in the domain of the system operators.