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Rules for Multidimensional Multirated Structures

Brian L. Evans
Organization: University of Texas
Department: Department of Electrical and Computer Engineering
URL: http://www.ece.utexas.edu/~bevans/
R. H. Bamberger
James H. McClellan
Organization: Georgia Tech
Journal / Anthology

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

Identifies a comprehensive set of compact rules and efficient algorithms for simplifying and rearranging structures common in multidimensional multirate signal processing. The authors extend the ID rules reported by Crochiere and Rabiner (1983), especially the many equivalent forms of cascades of upsamplers and downsamplers. They also include rules reported by other authors for completeness. The extension to mD 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 of a shuffling of input samples and a reshuffling of the separable operations. Based on the Smith form, the authors 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. The authors have encoded the knowledge in the commercially available Mathematica environment.

*Engineering > Signal Processing