POISSON WAVELETS APPLIED TO MODEL IDENTIFICATION

A novel wavelet transform is introduced based on the backward differen ce of the Poisson probability density function. This family of wavelet s is a function of one discrete and two continuous variables. The Pois son wavelet transform is useful for system identification, parameter e stimation and model validation. In particular, it is well-suited for l inear time-invariant systems that are modelled as combinations of deca ying exponentials with a single time delay. A fast computational algor ithm for computing the Poisson wavelet transform is developed using ca scaded first-order filters. The concepts are demonstrated on a three-t ank process and a simplified heat exchanger.