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- W4298366150 abstract "For the filtering of peaks in periodic signals, we specify polynomial filters that are optimally localized in space. The space localization of functions having an expansion in terms of orthogonal polynomials is thereby measured by a generalized mean value. Solving an optimization problem including this mean value, we determine those polynomials out of a polynomial space that are optimally localized. We give explicit formulas for these optimally space localized polynomials and determine in the case of the Jacobi polynomials the relation of the generalized mean value to the position variance of a well-known uncertainty principle. Further, we will consider the Hermite polynomials as an example on how to get optimally space localized polynomials in a non-compact setting. Finally, we investigate how the obtained optimal polynomials can be applied as filters in signal processing." @default.
- W4298366150 created "2022-10-02" @default.
- W4298366150 creator A5036671307 @default.
- W4298366150 date "2010-08-05" @default.
- W4298366150 modified "2023-10-18" @default.
- W4298366150 title "Optimally space localized polynomials with applications in signal processing" @default.
- W4298366150 doi "https://doi.org/10.48550/arxiv.1008.1525" @default.
- W4298366150 hasPublicationYear "2010" @default.
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