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Multiscale system identification and estimation

A formula for 'multiscale' representation of linear systems and stochastic processes is derived. The formula facilitates the synthesis of multiresolution analysis with linear systems theories. For example, it simplifies the use of scale-selective error metrics for system identification. This multiscale system identification framework yields closed form optimal solutions for non- parametric problems. Its 'wavelet-z-transform' version is a fast algorithm for the parametric case. Application of this method to nonlinear systems is also possible. In general, multiscale system identification is more effective for transient dynamics than classical time domain methods. Illustrations of this multiscale system identification method and comparison against time-domain approaches are presented.