Model reduction of multidimensional linear shift-invariant recursive systems using Pade´ techniques
Multidimensional Systems and Signal Processing
Multivariate partial Newton-Pade´ and Newton-Pade´ type approximants
Journal of Approximation Theory
How well can the concept of Padé approximant be generalized to the multivariate case?
Proceedings of the conference on Continued fractions and geometric function theory
Multidimensional Systems and Signal Processing
Multidimensional Digital Signal Processing
Multidimensional Digital Signal Processing
Orthogonality Measures and Applications in Systems Theory in One and More Variables
Large-Scale Scientific Computing
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It is well-known that model reduction techniques applied to stable multi-dimensional Linear Shift-Invariant (LSI) systems with Infinite-extent Impulse Response (IIR) do not necessarily guarantee a stable reduced system. Several conditions exist to check stability a posteriori. In this paper we outline a new technique that guarantees, a priori, that the system or filter is stable. In Section 1 we establish the necessary notation and definitions to deal with multi-dimensional systems and filters. Section 2 introduces the technique of multivariate Pade-type approximation and deals with stability. In Section 3 we illustrate the use of the newly proposed technique in filter design.