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The role of integer matrices in multidimensional multirate systems

Chen, Tsuhan and Vaidyanathan, P. P. (1993) The role of integer matrices in multidimensional multirate systems. IEEE Transactions on Signal Processing, 41 (3). pp. 1035-1047. ISSN 1053-587X. http://resolver.caltech.edu/CaltechAUTHORS:CHEieeetsp93d

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Abstract

The basic building blocks in a multidimensional (MD) multirate system are the decimation matrix M and the expansion matrix L. For the D-dimensional case these are D×D nonsingular integer matrices. When these matrices are diagonal, most of the one-dimensional (ID) results can be extended automatically. However, for the nondiagonal case, these extensions are nontrivial. Some of these extensions, e.g., polyphase decomposition and maximally decimated perfect reconstruction systems, have already been successfully made by some authors. However, there exist several ID results in multirate processing, for which the multidimensional extensions are even more difficult. An example is the development of polyphase representation for rational (rather than integer) sampling rate alterations. In the ID case, this development relies on the commutativity of decimators and expanders, which is possible whenever M and L are relatively prime (coprime). The conditions for commutativity in the two-dimensional (2D) case have recently been developed successfully in [1]. In the MD case, the results are more involved. In this paper we formulate and solve a number of problems of this nature. Our discussions are based on several key properties of integer matrices, including greatest common divisors and least common multiples, which we first review. These properties are analogous to those of polynomial matrices, some of which have been used in system theoretic work (e.g., matrix fraction descriptions, coprime matrices, Smith form, and so on).


Item Type:Article
Additional Information:© Copyright 1993 IEEE. Reprinted with permission. Manuscript received August 21, 1991; revised March 13, 1992. This work was supported in part by National Science Foundation Grants MIP 8604456, MIP 8919196, and by matching funds from Tektronix, Inc., and Rockwell International.
Subject Keywords:filtering and prediction theory; matrix algebra; multidimensional digital filters; signal processing
Record Number:CaltechAUTHORS:CHEieeetsp93d
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:CHEieeetsp93d
Alternative URL:http://dx.doi.org/10.1109/78.205712
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9914
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:26 Mar 2008
Last Modified:26 Dec 2012 09:54

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