Article

Multidimensional Systems and Signal Processing

, Volume 25, Issue 3, pp 447-471

Multidimensional IIR filters and robust rational interpolation

  • Annie CuytAffiliated withDepartment of Mathematics and Computer Science, University of Antwerp (CMI) Email author 
  • , Oliver Salazar CelisAffiliated withDepartment of Mathematics and Computer Science, University of Antwerp (CMI)
  • , Maryna LukachAffiliated withDepartment of Mathematics and Computer Science, University of Antwerp (CMI)

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Abstract

It is well-known that IIR filters can have a much lower order than FIR filters with the same performance. On the downside is that the implementation of an IIR filter is an iterative procedure while that of an FIR filter is a one-shot computation. But in higher dimensions IIR filters are definitely more attractive. We offer a technique where the filter’s performance specifications, stability constraints, its convergence speed and a protection against possible adverse effects of perturbations are all included in the design from the start. The technique only needs an off-the-shelf LP solver because the filter is obtained as a Chebyshev center of a convex polytope. The method deals with general non-causal non-separable filters.

Keywords

Multidimensional digital filters Non-causal IIR Linear programming Quadratic programming Rational approximation