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 functionthanks 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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