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Signal Processing Magazine, IEEE

Issue 3 • Date July 1991

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  • Adaptive polynomial filters

    Publication Year: 1991 , Page(s): 10 - 26
    Cited by:  Papers (220)  |  Patents (8)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1447 KB)  

    Adaptive nonlinear filters equipped with polynomial models of nonlinearity are explained. The polynomial systems considered are those nonlinear systems whose output signals can be related to the input signals through a truncated Volterra series expansion or a recursive nonlinear difference equation. The Volterra series expansion can model a large class of nonlinear systems and is attractive in adaptive filtering applications because the expansion is a linear combination of nonlinear functions of the input signal. The basic ideas behind the development of gradient and recursive least-squares adaptive Volterra filters are first discussed. Adaptive algorithms using system models involving recursive nonlinear difference equations are then treated. Such systems may be able to approximate many nonlinear systems with great parsimony in the use of coefficients. Also discussed are current research trends and new results and problem areas associated with these nonlinear filters. A lattice structure for polynomial models is described.<> View full abstract»

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  • Orthogonal approaches to time-series analysis and system identification

    Publication Year: 1991 , Page(s): 29 - 43
    Cited by:  Papers (46)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1276 KB)  

    Some recent, efficient approaches to nonlinear system identification, ARMA modeling, and time-series analysis are described and illustrated. Sufficient detail and references are furnished to enable ready implementation, and examples are provided to demonstrate superiority over established classical techniques. The ARMA identification algorithm presented does not require a priori knowledge of, or assumptions about, the order of the system to be identified or signal to be modeled. A suboptimal, recursive, pairwise search of the orthogonal candidate data records is conducted, until a given least-squares criterion is satisfied. In the case of nonlinear systems modeling, discrete-time Volterra series is stressed, or rather a more efficient parallel-cascade approach. The model is constructed by adding parallel paths (each consisting of the cascade of dynamic linear and static nonlinear systems). In the case of time-series analysis, a non-Fourier sinusoidal series approach is stressed. The relevant frequencies are estimated by an orthogonal search procedure. A search of the candidate sinusoids is conducted until a given mean-square criterion is satisfied.<> View full abstract»

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IEEE Signal Processing Magazine publishes tutorial-style articles on signal processing research and applications, as well as columns and forums on issues of interest.

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Editor-in-Chief
Min Wu
University of Maryland, College Park
United States 

http://www/ece.umd.edu/~minwu/