On necessary and sufficient conditions for perfect reconstruction multidimensional delay chain systems

Author

Xia, Xiang-Gen ; Suter, Bruce W. ; Oxley, Mark E.

Author_Institution

Dept. of Electr. & Comput. Eng., Air Force Inst. of Technol., Wright-Patterson AFB, OH, USA

Volume

43

Issue

6

fYear

1995

fDate

6/1/1995 12:00:00 AM

Firstpage

1515

Lastpage

1519

Abstract

We present some necessary and sufficient conditions for a perfect reconstruction (PR) modified multidimensional (MD) delay chain system. With these results, one is able to systematically check if a D-dimensional delay chain system with a D×D sampling matrix M and a D×D delay matrix L has a PR property in a simpler way than before, where the matrix module operations are avoided. Moreover, given a D×D sampling matrix M, in many cases one can determine all possible D×D delay matrices L so that the delay chain systems with the sampling matrix M have a PR property. Several examples are provided. We also present a method to generate D×D sampling and delay matrices M and L such that their corresponding traditional MD delay chain systems are PR

Keywords

delay systems; matrix algebra; multidimensional systems; signal reconstruction; signal sampling; MD delay chain systems; delay matrix; multidimensional delay chain systems; necessary conditions; perfect reconstruction systems; sampling matrix; sufficient conditions; Delay systems; Filter bank; Image reconstruction; Image sampling; Mathematics; Multidimensional systems; Sampling methods; Sufficient conditions; Symmetric matrices; Unmanned aerial vehicles;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.388867

Filename

388867