TITLE:
AAK Theorem and a Design of Multidimensional BIBO Stable Filters
AUTHORS:
Bossoto Bossoto, Gabriel Bissanga
KEYWORDS:
Multidimensional Filter, Design, BIBO Stability, Optimal, AAK Theorem, Transfer Function, Hankel Matrix
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.14 No.2,
March
26,
2024
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.