The role of integer matrices in multidimensional multirate systems

Author

Chen, Tsuhan ; Vaidyanathan, P.P.

Author_Institution

Dept. of Electr. Eng., California Inst. of Technol., Pasadena, CA, USA

Volume

41

Issue

3

fYear

1993

fDate

3/1/1993 12:00:00 AM

Firstpage

1035

Lastpage

1047

Abstract

Various theoretical issues in multidimensional (m-D) multirate signal processing are formulated and solved. In the problems considered, the decimation matrix and the expansion matrix are nondiagonal, so that extensions of 1-D results are nontrivial. The m -D polyphase implementation technique for rational sampling rate alterations, the perfect reconstruction properties for the m-D delay-chain systems, and the periodicity matrices of decimated m-D signals (both deterministic and statistical) are treated. The discussions are based on several key properties of integer matrices, including greatest common divisors and least common multiples. These properties are reviewed

Keywords

filtering and prediction theory; matrix algebra; multidimensional digital filters; signal processing; decimation matrix; expansion matrix; filter banks; greatest common divisors; integer matrices; least common multiples; multidimensional delay-chain systems; multidimensional multirate systems; perfect reconstruction properties; periodicity matrices; polyphase implementation; signal processing; Delay systems; Filter bank; Image reconstruction; Matrix decomposition; Multidimensional signal processing; Multidimensional systems; Polynomials; Sampling methods;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.205712

Filename

205712