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AAK Theorem and a Design of Multidimensional BIBO Stable Filters
Faculty of Sciences and Technology, Marien Ngouabi University, Brazzaville, Congo
Faculty of Sciences and Technology, Marien Ngouabi University, Brazzaville, Congo
- 1 Faculty of Sciences and Technology, Marien Ngouabi University, Brazzaville, Congo
- 2 Faculty of Sciences and Technology, Marien Ngouabi University, Brazzaville, Congo
Open Journal of Discrete Mathematics·Volume 14 (2024)·Pages 9–15·Published 26 March 2024·DOI10.4236/ojdm.2024.142002
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Abstract
Rational approximation theory occupies a significant place in signal processing and systems theory. This research paper proposes an optimal design of BIBO stable multidimensional Infinite Impulse Response filters with a realizable (rational) transfer function thanks to the Adamjan, Arov and Krein (AAK) theorem. It is well known that the one dimensional AAK results give the best approximation of a polynomial as a rational function in the Hankel semi norm. We suppose that the Hankel matrix associated to the transfer function has a finite rank.
KeywordsMultidimensional FilterDesignBIBO StabilityOptimalAAK TheoremTransfer FunctionHankel Matrix
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