Stability analysis of 1-D and 2-D fixed-point state-space digital filters using any combination of overflow and quantization nonlinearities

Author

Kar, Haranath ; Singh, Vimal

Author_Institution

Dept. of Electron. Eng., M.N.R. Eng. Coll., Allahahad, India

Volume

49

Issue

5

fYear

2001

fDate

5/1/2001 12:00:00 AM

Firstpage

1097

Lastpage

1105

Abstract

A new criterion, together with its frequency-domain interpretation for the global asymptotic stability of zero-input one-dimensional (1-D) state-space digital filters under various combinations of overflow and quantization nonlinearities and for the situation where quantization occurs after summation only, is presented. A condition in closed form involving solely the parameters of the state transition matrix for the nonexistence of limit cycles in second-order digital filters is derived. Improved versions of some of the stability results due to Leclerc and Bauer (1994) are established. Finally, the approach is extended to two-dimensional (2-D) digital filters described by the Roesser and the Fornasini-Marchesini second local state-space models

Keywords

asymptotic stability; circuit stability; filtering theory; fixed point arithmetic; matrix algebra; nonlinear filters; quantisation (signal); state-space methods; two-dimensional digital filters; 1D fixed-point state-space digital filters; 2D fixed-point state-space digital filters; closed form condition; global asymptotic stability; overflow nonlinearity; quantization nonlinearity; second local state-space models; second-order digital filters; stability analysis; state transition matrix; zero-input 1D state-space digital filters; Asymptotic stability; Digital filters; Frequency domain analysis; Limit-cycles; Lyapunov method; Quantization; Stability analysis; Symmetric matrices; System testing; Two dimensional displays;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.917812

Filename

917812