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Rules for Multidimensional Multirate Structures

Brian L. Evans
Organization: University of Texas
Department: Department of Electrical and Computer Engineering
URL: http://www.ece.utexas.edu/~bevans/
Journal / Anthology

IEEE Transactions on Signal Processing
Year: 1994
Volume: 42
Issue: 4
Page range: 762-771

This paper identifies a comprehensive set of compact rules and efficient algorithms for simplifying and rearranging structures common in multidimensional multirate signal processing. We extend the 1-D rules reported by Crochiere and Rabiner, especially the many equivalent forms of cascades of upsamplers and downsamplers. We also include rules reported by other authors for completeness. The extension to m-D is based primarily on the Smith form decomposition of resampling (nonsingular integer square) matrices. The Smith form converts non-separable multidimensional operations into separable ones by means a shuffling of input samples and a reshuffling of the separable operations. Based on the Smith form, we have developed algorithms for 1) computing coset vectors; 2) finding greatest common sublattices; 3) simplifying cascades of up/downsampling operations. The algorithms and rules are put together in a form that can be implemented efficiently in a symbolic algebra package. We have encoded the knowledge in the commercially available Mathematica environment.

*Engineering > Signal Processing