HomeChair: Giovanni L. Sicuranza, University of Trieste, Italy
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Alberto Carini, Universite di Trieste (Italy)
Giovanni L. Sicuranza, Universite di Trieste (Italy)
V. John Mathews, University of Utah (U.S.A.)
This paper presents two theorems for the exact inversion and the pth order inversion of a wide class of causal, discrete-time, nonlinear systems. The nonlinear systems we consider are described by the input-output relationship [equation omitted] where g[] and f[] are causal, discrete-time and nonlinear operators and the inverse function [equation omitted] exists. The exact inverse of such systems is given by [equation omitted]. Similarly, the pth order inverse is given by [equation omitted] where [equation omitted] is the pth order inverse of [equation omitted].
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Kelly K. Johnson, The University of Texas at Austin (U.S.A.)
Irwin W. Sandberg, The University of Texas at Austin (U.S.A.)
We consider stability properties of discrete-time bilinear filters. Simple sufficient conditions are given for bounded-input bounded-output stability (with not necessarily zero initial conditions), lp stability, and three other important types of stability. In particular, conditions are given under which asymptotically periodic inputs produce asymptotically periodic outputs with the same period. Related results are given for quadratic filters.
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Yoshinobu Kajikawa, Kansai University (Japan)
Yasuo Nomura, Kansai University (Japan)
In this paper, we propose the summational projection algorithm which has the convergence properties of high speed and high accuracy under high noise and colored input signal. We particularly discuss the adaptive algorithm for the adaptive Volterra filter which can be used to identify and design nonlinear systems. The proposal algorithm realizes the these convergence properties by controlling the length of the block in the updating algorithm. First of all, we present the general type of the proposed summational projection algorithm. Next, we show that the proposal algorithm is effective in the identification of nonlinear systems. Finally, we apply the proposed algorithm to the design method of a nonlinear inverse system.
ns970433.pdf (Scanned) ns970433.pdf (From Postscript) TOPIrwin W. Sandberg, The University of Texas at Austin (U.S.A.)
We consider causal time-invariant nonlinear input-output maps that take a set of bounded functions into a set of real-valued functions, and we give criteria under which these maps can be uniformly approximated arbitrarily well using a certain structure consisting of a not-necessarily linear dynamic part followed by a nonlinear memoryless section that may contain sigmoids or radial basis functions, etc. As an application of the results, we show that system maps of the type addressed can be uniformly approximated arbitrarily well by doublyfinite Volterra-series approximants if and only if these maps have approximately-finite memory and satisfy certain continuity conditions. Corresponding results have also been obtained for (not necessary causal) multivariable input-output maps. Such multivariable maps axe of interest in connection with image processing.
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Gil M. Raz, University of Wisconsin-Madison (U.S.A.)
Barry D. Van Veen, University of Wisconsin-Madison (U.S.A.)
A diagonal coordinate representation for Volterra filters is developed and exploited to derive efficient Volterra filter implementations for processing carder based input signals. In the diagonal coordinate representation the output is expressed as a sum of linear filters applied to modified input signals. Hence, linear filtering methods are employed to implement the nonlinear filter on a baseband version of the input. Downsampling is then used to reduce computational complexity.
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Mounir Ghogho, ENSEEMT-INP (France)
Souad Meddeb, ENSEEMT-INP (France)
Jamila Bakkoury, ENSEEMT-INP (France)
This paper addresses the problem of time-varying (TV) nonlinear system identification. We focus on a class of (almost) periodically TV Volterra series. Such a model is shown to well describe mobile satellite channels which are structured as a time-invariant (TIV) filter cascaded with a TIV zero-memoryless nonlinearity (ZMNL) and a TV linear filter. The nonlinearity distortion is due to the on-board satellite amplifier. The TV filter characterizes fading multipath in mobile environment. A least squares estimate of the TV Volterra kernels with finite memory is first derived for any arbitrary channel input. Then, closed form solutions of the Volterra kernels are derived for symmetrically circular input sequences. The theoretical results are illustrated by simulations.
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