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    Wavelet-Based Transformations for Nonlinear Signal Processing

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    Author
    Nowak, Robert David; Baraniuk, Richard G.
    Date
    1999-07-01
    Abstract
    Nonlinearities are often encountered in the analysis and processing of real-world signals. In this paper, we introduce two new structures for nonlinear signal processing. The new structures simplify the analysis, design, and implementation of nonlinear filters and can be applied to obtain more reliable estimates of higher-order statistics. Both structures are based on a two-step decomposition consisting of a linear orthogonal signal expansion followed by scalar polynomial transformations of the resulting signal coefficients. Most existing approaches to nonlinear signal processing characterize the nonlinearity in the time domain or frequency domain; in our framework any orthogonal signal expansion can be employed. In fact, there are good reasons for characterizing nonlinearity using more general signal representations like the wavelet transform. Wavelet expansions often provide very concise signal representation and thereby can simplify subsequent nonlinear analysis and processing. Wavelets also enable local nonlinear analysis and processing in both time and frequency, which can be advantageous in non-stationary problems. Moreover, we show that the wavelet domain offers significant theoretical advantages over classical time or frequency domain approaches to nonlinear signal analysis and processing.
    Description
    Journal Paper
    Citation
    R. D. Nowak and R. G. Baraniuk, "Wavelet-Based Transformations for Nonlinear Signal Processing," IEEE Transactions on Signal Processing, vol. 47, no. 7, 1999.
    Published Version
    http://dx.doi.org/10.1109/78.771035
    Keyword
    Temporary; Wavelet based Signal/Image Processing; Temporary
    Type
    Journal article
    Citable link to this page
    https://hdl.handle.net/1911/20162
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    Managed by the Digital Scholarship Services at Fondren Library, Rice University
    Physical Address: 6100 Main Street, Houston, Texas 77005
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    Site Map