Algebra of multidimensional multirate structures
Richard Tolimieri, Myoung H. An · International Journal of Imaging Systems and Technology · 1996
In several recent papers, the Aryabhatta/Bezout identity and the Smith form for integer matrices were applied to the problem of determining a complete set of product rules for the algebra generated by downsampling, upsampling, and shift operators in multidimensions. In this work we will derive these results emphasizing properties of the indexing group Zn. This effort will substantially simplify several previously derived results by attaching them directly to group concepts and highlighting the unifying role played by direct sum decompositions and short exact sequences. In this way we present a theory whose basic structures are the same as those used to describe data partitioning for the discrete Fourier transform. © 1996 John Wiley & Sons, Inc.