IEEE Signal Processing Letters, vol. 4, no. 11, pp. 313-316, Nov. 1997

Designing Commutative Cascades of Multidimensional Upsamplers and Downsamplers

Brian L. Evans

Department of Electrical and Computer Engineering, Engineering Science Building, The University of Texas at Austin, Austin, TX 78712-1084 USA
bevans@ece.utexas.edu

Abstract

In multiple dimensions, the cascade of an upsampler by L and a downsampler by L commutes if and only if the integer matrices L and M are right coprime and L M = M L. This paper presents algorithms to design L and M that yield commutative upsampler/dowsampler cascades. We prove that commutativity is possible if the Jordan canonical form of the rational (resampling) matrix R = L M^-1 is equivalent to the Smith-McMillan form of R. A necessary condition for this equivalence is that R has an eigendecomposition and the eigenvalues are rational.

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Last Updated 11/19/98.