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On an asymptotic analysis of polynomial approximation to halfband filters |
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| Authors: | Charles A Micchelli Jianzhong Wang Yi Wang |
| Institution: | 1. Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China 2. Department of Mathematics and Statistics, State University of New York, The University at Albany, Albany, NY, 12222, USA 3. Department of Mathematics and Statistics, Sam Houston State University, P.O. Box 2206, Huntsville, TX, 77341-2206, USA 4. Department of Mathematics, Auburn University at Montgomery, P.O. Box 244023, Montgomery, AL, 36124-4023, USA |
| 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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