Sufficient condition for state-space representation of N-D discrete-time lossless bounded real matrix and N-D stability of Mansour matrix

Author

Matsumoto, N. ; Anderson, B.D.O. ; Mansour, M.

Author_Institution

Dept. of Electron. & Commun., Meiji Univ., Kawasaki, Japan

Volume

37

Issue

9

fYear

1990

fDate

9/1/1990 12:00:00 AM

Firstpage

1151

Lastpage

1157

Abstract

The definition of an N-D discrete-time lossless bounded real (DTLBR) matrix and sufficient conditions on a state-space representation to correspond to an N-D DTLBR matrix are given. Based on these sufficient conditions, it is shown that the transfer function of the n-D lattice filter, which is obtained from a stable 1-D lattice filter by replacing each delay element z with z_i (i=1,2,.....,n), becomes a n-D DTLBR function. From this fact, an n×n Mansour matrix (which is an A-matrix of the state-space representation of a 1-D lattice filter) is proved to be stable for any dimension up to n, if it is stable in the one-dimensional case

Keywords

digital filters; discrete time systems; matrix algebra; stability; state-space methods; transfer functions; A-matrix; DTLBR matrix; Mansour matrix; N-D discrete-time lossless bounded real matrix; N-D stability; delay element; n-D lattice filter; stable 1-D lattice filter; state-space representation; transfer function; Adaptive filters; Circuits; Filter bank; IIR filters; Lattices; Signal processing algorithms; Speech processing; Stability; Sufficient conditions; System identification;

fLanguage

English

Journal_Title

Circuits and Systems, IEEE Transactions on

Publisher

ieee

ISSN

0098-4094

Type

jour

DOI

10.1109/31.57603

Filename

57603