%0 Journal Article
%T AAK Theorem and a Design of Multidimensional BIBO Stable Filters
%A Bossoto Bossoto
%A Gabriel Bissanga
%J Open Journal of Discrete Mathematics
%P 9-15
%@ 2161-7643
%D 2024
%I Scientific Research Publishing
%R 10.4236/ojdm.2024.142002
%X Rational approximation theory occupies a significant
place in signal processing and systems theory. This research paper proposes an
optimal design of BIBO<span><span><span style=\"font-family:;\" \"=\"\"> stable multidimensional Infinite Impulse Response
filters with a realizable (rational) transfer function<img src=\"Edit_1c782536-a8f1-4220-86a7-6204b517a24b.jpg\" alt=\"\" /> </span><span style=\"color:black;\"><span></span></span></span></span><span><span><span style=\"font-family:;\" \"=\"\"><span> </span>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.</span></span></span>
%K Multidimensional Filter
%K Design
%K BIBO Stability
%K Optimal
%K AAK Theorem
%K Transfer Function
%K Hankel Matrix
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=132064