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On an asymptotic analysis of polynomial approximation to halfband filters

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Abstract

In this paper we provide information about the asymptotic properties of polynomial filters which approximate the ideal filter. In particular, we study this problem in the special case of polynomial halfband filters. Specifically we estimate the error between a polynomial filter and an ideal filter and show that the error decays exponentially fast. For the special case of polynomial halfband filters, our n-th root asymptotic error estimates are sharp.

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Authors and Affiliations

  1. Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China

    Charles A. Micchelli

  2. Department of Mathematics and Statistics, State University of New York, The University at Albany, Albany, NY, 12222, USA

    Charles A. Micchelli

  3. Department of Mathematics and Statistics, Sam Houston State University, P.O. Box 2206, Huntsville, TX, 77341-2206, USA

    Jianzhong Wang

  4. Department of Mathematics, Auburn University at Montgomery, P.O. Box 244023, Montgomery, AL, 36124-4023, USA

    Yi Wang

Authors
  1. Charles A. Micchelli
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  2. Jianzhong Wang
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  3. Yi Wang
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Corresponding author

Correspondence to Yi Wang.

Additional information

Communicated by Yuesheng Xu.

C.A. Micchelli was partially supported by the NSF grant DMS 0712827 and AFOSR FA9550-09-0511.

J. Wang was partially supported by the NSF grant DMS 0712925.

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Micchelli, C.A., Wang, J. & Wang, Y. On an asymptotic analysis of polynomial approximation to halfband filters. Adv Comput Math 38, 601–622 (2013). https://doi.org/10.1007/s10444-011-9251-y

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  • DOI: https://doi.org/10.1007/s10444-011-9251-y

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