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AAK Theorem and a Design of Multidimensional BIBO Stable Filters

DOI: 10.4236/ojdm.2024.142002, PP. 9-15

Keywords: Multidimensional Filter, Design, BIBO Stability, Optimal, AAK Theorem, Transfer Function, Hankel Matrix

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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.

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