Relationship between an LPTV system and the equivalent LTI MIMO structure

Author

McLernon, D.C.

Author_Institution

Sch. of Electron. & Electr. Eng., Univ. of Leeds, UK

Volume

150

Issue

3

fYear

2003

fDate

6/20/2003 12:00:00 AM

Firstpage

133

Lastpage

141

Abstract

It is understood how to transform a linear periodically time-varying (LPTV) filter/ difference equation into an equivalent multiple-input/multiple-output (MIMO) structure, or transfer matrix, with linear time-invariant (LTI) elements, but no published method exists for the reverse operation. The paper presents a technique to transform from the LTI MIMO structure to the original single-input/single-output LPTV difference equation and discusses its implications. In addition, it is shown how this new result is then used to represent parallel and cascade connections of LPTV systems as single LPTV filters, implement order reduction of an LPTV difference equation, and finally obtain an LPTV difference equation representation that is equivalent to an LPTV state-space structure.

Keywords

MIMO systems; difference equations; filtering theory; linear systems; matrix algebra; state-space methods; time-varying filters; time-varying systems; LPTV filters; LPTV state-space structure; LPTV system; LTI MIMO structure; SISO LPTV difference equation; cascade connections; difference equation; linear periodically time-varying filter; linear time-invariant elements; multiple-input/multiple-output structure; order reduction; parallel connections; single-input/single-output difference equation; transfer matrix;

fLanguage

English

Journal_Title

Vision, Image and Signal Processing, IEE Proceedings -

Publisher

iet

ISSN

1350-245X

Type

jour

DOI

10.1049/ip-vis:20030509

Filename

1216823