Title
An inhomogeneous uncertainty principle for digital low-pass filters
Abbreviated Journal Title
J. Fourier Anal. Appl.
Keywords
digital low-pass filter; filter efficiency; uncertainty principle; trigonometric polynomials; WAVELETS; Mathematics, Applied
Abstract
This article introduces an inhomogeneous uncertainty principle for digital low-pass filters. The measure for uncertainty is a product of two factors evaluating the frequency selectivity in comparison with the ideal filter and the effective length of the filter in the digital domain, respectively. We derive a sharp lower bound for this product in the class of filters with so-called finite effective length and show the absence of minimizers. We find necessary and certain sufficient conditions to identify minimizing sequences. When the class of filters is restricted to a given maximal length, we show the existence of an uncertainty minimizer. The uncertainty product of such minimizing filters approaches the unrestricted infimum as the filter length increases. We examine the asymptotics and explicitly construct a sequence of finite-length filters with the same asymptotics as the sequence of finite-length minimizers.
Journal Title
Journal of Fourier Analysis and Applications
Volume
12
Issue/Number
2
Publication Date
1-1-2006
Document Type
Article
Language
English
First Page
181
Last Page
211
WOS Identifier
ISSN
1069-5869
Recommended Citation
"An inhomogeneous uncertainty principle for digital low-pass filters" (2006). Faculty Bibliography 2000s. 5967.
https://stars.library.ucf.edu/facultybib2000/5967
Comments
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