Algebra of multidimensional multirate structures

✍ Scribed by Richard Tolimieri; Myoung An

• Publisher: John Wiley and Sons
• Year: 1996
• Tongue: English
• Weight: 402 KB
• Volume: 7
• Category: Article
• ISSN: 0899-9457
• DOI: 10.1002/(sici)1098-1098(199624)7:4<421::aid-ima16>3.0.co;2-y

✦ Synopsis

In several recent papers, the AryabhattaBezout 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 2". 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. 0 1996 John Wiley & Sons, Inc.