Rules for multidimensional multirate structures
Evans, B.L.; Bamberger, R.H.; McClellan, J.H.
Signal Processing, IEEE Transactions on
Volume 42, Issue 4, Apr 1994 Page(s):762 - 771
Digital Object Identifier 10.1109/78.285641
Summary: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 1D
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 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
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