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    Tensor Product Basis Approximations for Volterra Filters

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    Author
    Nowak, Robert David; Van Veen, Barry D.
    Date
    1996-02-01
    Abstract
    This paper studies approximations for a class of nonlinear filters known as Volterra filters. Although the Volterra filter provides a relatively simple and general representation for nonlinear filtering, often it is highly over-parameterized. Due to the large number of parameters, the utility of the Volterra filter is limited. The over-parameterization problem is addressed in this paper using a tensor product basis approximation (TPBA). In many cases a Volterra filter may be well approximated using the TPBA with far fewer parameters. Hence, the TPBA offers considerable advantages over the original Volterra filter in terms of both implementation and estimation complexity. Furthermore, the TPBA provides useful insight into the filter response. This paper studies the crucial issue of choosing the approximation basis. Several methods for designing an appropriate approximation basis and error bounds on the resulting mean-square output approximation error are derived. Certain methods are shown to be nearly optimal.
    Description
    Journal Paper
    Citation
    R. D. Nowak and B. D. Van Veen, "Tensor Product Basis Approximations for Volterra Filters," IEEE Transactions on Image Processing, 1996.
    Published Version
    http://dx.doi.org/10.1109/78.482010
    Keyword
    Temporary; Wavelet based Signal/Image Processing; Temporary
    Type
    Journal article
    Citable link to this page
    https://hdl.handle.net/1911/20157
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    • DSP Publications [508]
    • ECE Publications [1468]

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    Managed by the Digital Scholarship Services at Fondren Library, Rice University
    Physical Address: 6100 Main Street, Houston, Texas 77005
    Mailing Address: MS-44, P.O.BOX 1892, Houston, Texas 77251-1892
    Site Map