 |
|
|
|
|
 |
|
|
Rules for Multidimensional Multirate Structures
|
|
|
|
|
|
| Organization: | University of Texas |
| Department: | Department of Electrical and Computer Engineering |
|
|
|
|
|
|
| IEEE Transactions on Signal Processing |
|
|
|
|
|
|
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.
|
|
|
|
|
|
|
|
For the newest resources, visit Wolfram Repositories and Archives »
