The wavelet network [22, 23] has been introduced as a special feedforward neural network supported by the wavelet theory. Such network can be directly used in function approximation problems, and consequently can be applied to nonlinear system modeling by means of nonlinear black-box identification. In this paper the construction of feedforward neural networks is discussed from both identification and regressor selection points of view. This reveals that the wavelet network structure is well suited for developing constructive methods for feedforward networks. An efficient initialization procedure of the wavelet network based on the orthogonal least squares (OLS) method is then proposed. The efficiency of the wavelet network and the proposed procedure for nonlinear system modeling is illustrated by a numerical example.

In earlier work [Pati and Krishnaprasad 1992] it was shown that rational wavelet frame decompositions of the Hardy space H 2 (\Pi + ) may be used to efficiently capture time-frequency localized behavior of stable linear systems, for purposes of system identification and model-reduction. In this paper we examine the problem of efficient computation of low-order rational wavelet approximations of stable linear systems. We describe a variant of the Matching Pursuit algorithm [Mallat and Zhang 1992] that utilizes successive projections onto two-dimensional subspaces to construct rational wavelet approximants. The methods described here are illustrated by means of both simulations and experimental results. 1 Introduction and Background It is well-known that rational functions play a central role in linear systems theory due to the equivalence of rational transfer functions and finitedimensional linear time-invariant (LTI) systems. In the context of linear system theory, rational approx...

. Using the Daubechies wavelet theory we establish rational wavelet decompositions of the Hardy--Sobolev classes on the half-plane. The decay of wavelet coe#cients is analyzed and error bounds for approximation are given. We give applications to the modeling of linear systems and to the model reduction of infinite-dimensional systems. Key words. wavelets, frames, atomic decompositions, matching pursuits, infinite-dimensional systems, Hardy--Sobolev spaces AMS subject classifications. 41, 93 PII. S0363012996297339 1. Introduction. 1.1. Notation and conventions. C+ = {s = x + iy : x > 0} right half-plane, I = {iy : y # R} imaginary axis. For f belonging to L 2 (R) the Fourier transform f is defined using the following convention: f(#) = Z # -# f(t)e -i#t dt. For g belonging to L 2 ((0, #)) we write G = (Lg)(s) for the Laplace transform of g: G(s) = (Lg)(s) = Z # 0 g(t)e -st dt. H 2 (C+ ) denotes the Hardy space of functions F (s) analytic in the right half-p...

: The wavelet network [22, 23] has been introduced as a special feedforward neural network supported by the wavelet theory. Such network can be directly used in function approximation problems, and consequently can be applied to nonlinear system modeling by means of nonlinear black-box identification. In this paper the construction of feedforward neural networks is discussed from both identification and regressor selection points of view. This reveals that the wavelet network structure is well suited for developing constructive methods for feedforward networks. An efficient initialization procedure of the wavelet network based on the orthogonal least squares (OLS) method is then proposed. The efficiency of the wavelet network and the proposed procedure for nonlinear system modeling is illustrated by a numerical example. Key-words: neural network, wavelet transform, nonlinear system identification, function approximation. (R'esum'e : tsvp) This study was performed during the author's ...

In this thesis a new signal processing technique is presented. This technique exploits the use of pulses as the signalling mechanism. This Palmo 1 signalling method applied to signal processing is novel, combining the advantages of both digital and analogue techniques. Pulsed signals are robust, inherently low-power, easily regenerated, and easily distributed across and between chips. The Palmo cells used to perform analogue operations on the pulsed signals are compact, fast, simple and programmable.

Title of Dissertation: Analysis and Synthesis of Distributed Systems Yan Zhuang, Doctor of Philosophy, 1994 Dissertation directed by: Professor John S. Baras Martin Marietta Chair in Systems Engineering Department of Electrical Engineering University of Maryland, College Park We first model and analyze distributed systems including distributed sen- sors and actuators. We then consider identification of distributed systems via adaptive wavelet neural networks (AWNNs) by taking advantage of the multires- olution property of wavelet transforms and the parallel computational structure of neural networks. A new systematic approach is developed in this dissertation to construct an optimal discrete orthonormal wavelet basis with compact sup- port for spanning the subspaces employed for system identification and signal representation. We then apply a backpropagation algorithm to train the network to approximate the system. Filter banks for parameterizing wavelet systems are studied. An analog VLSI implementation architecture of the AWNN is also given in this dissertation. This work is applicable to signal representation and compression under optimal orthonormal wavelet bases in addition to progressive system identification and modeling. We anticipate that this work will find future applications in signal processing and intelligent systems.