Multidimensional Nonlinear Schur Parametrization of NonGaussian Stochastic Signals Part Three: Low-Complexity Staircase Solution

  • Authors:

  • Jan Zarzycki

  • Affiliations:

  • Signal Theory Section, Department Electrical Engineering, Wroclaw University of Technology, W.Wyspianskiego 27, 50-370 Wroclaw, Poland/ jan.zarzycki@pwr.wroc.pl

  • Venue:
  • Multidimensional Systems and Signal Processing
  • Year:
  • 2004

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Abstract

In the first part [2] of this set of papers we stated the multidimensional nonlinear Schur parametrization problem for higher-order stochastic sequences. In the second part [1] we proposed the recursive solution to this problem, deriving the general multidimensional nonlinear Schur parametrization algorithm. The goal of this paper is to introduce a low-complexity solution to the nonlinear Schur parametrization problem, following from a multidimensional generalization of the two-indexed matrix extension problem. To obtain the solution, we derive a global multidimensional nonlinear Schur algorithm, then formulate and prove generalized staircase extension and interpolation theorems. The obtained results allow to achieve a considerable complexity reduction of the Schur parametrization algorithms for higher-order stochastic sequences as well as of orthogonal nonlinear approximate filters (of␣ band-structure) of the Volterra–Wiener class.