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Regressor Selection and Wavelet Network Construction
 IN 32ND CONFERENCE ON DECISION AND CONTROL
, 1993
"... 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 blackbox identification. ..."
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Cited by 7 (1 self)
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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 blackbox 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.
A Fast Recursive Algorithm for System Identification and Model Reduction Using Rational Wavelets
, 1993
"... 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 timefrequency localized behavior of stable linear systems, for purposes of system identification and modelreduction. In this ..."
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Cited by 4 (0 self)
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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 timefrequency localized behavior of stable linear systems, for purposes of system identification and modelreduction. In this paper we examine the problem of efficient computation of loworder 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 twodimensional 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 wellknown that rational functions play a central role in linear systems theory due to the equivalence of rational transfer functions and finitedimensional linear timeinvariant (LTI) systems. In the context of linear system theory, rational approx...
A Construction Of Rational Wavelets And Frames In HardySobolev Spaces With Applications To System Modeling
, 1998
"... . Using the Daubechies wavelet theory we establish rational wavelet decompositions of the HardySobolev classes on the halfplane. 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 reduct ..."
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Cited by 4 (1 self)
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. Using the Daubechies wavelet theory we establish rational wavelet decompositions of the HardySobolev classes on the halfplane. 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 infinitedimensional systems. Key words. wavelets, frames, atomic decompositions, matching pursuits, infinitedimensional systems, HardySobolev spaces AMS subject classifications. 41, 93 PII. S0363012996297339 1. Introduction. 1.1. Notation and conventions. C+ = {s = x + iy : x > 0} right halfplane, 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 halfp...
Productique
"... : 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 blackbox identificatio ..."
Abstract
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: 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 blackbox 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. Keywords: neural network, wavelet transform, nonlinear system identification, function approximation. (R'esum'e : tsvp) This study was performed during the author's ...
Palmo: a novel pulsed based signal processing technique for programmable mixedsignal VLSI
, 1998
"... 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, i ..."
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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 lowpower, 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.
Analysis and Synthesis of Distributed Systems
, 1994
"... 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 an ..."
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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.