A NEW ALGORITHM TO TEST THE STABILITY OF 2-D DIGITAL RECURSIVE FILTERS

被引:5
作者
BARRET, M
BENIDIR, M
机构
[1] Supélec, Campus de Metz, 2 Rue É. Belin, Technopôle 2000
[2] Université de Paris-Sud, 91192 Gif-sur-Yvette, L2S-Supelec, Plateau de Moulon
关键词
IIR FILTER; 2-DIMENSIONAL SIGNAL PROCESSING; DIGITAL FILTER; DISCRETE-TIME SYSTEM STABILITY; POLYNOMIAL ZERO DISTRIBUTION; RESULTANT; SUBRESULTANT; BEZOUTIAN; DISPLACEMENT RANK OF THE SCHUR-COHN MATRIX;
D O I
10.1016/0165-1684(94)90107-4
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
Any algorithm for testing the stability of 2-D digital recursive filters has to process a 2-D polynomial of degree n and m with respect to each variable. The number of computations needed by the algorithm can be expressed as a polynomial of the variables n and m. The total degree of this polynomial defines the complexity order of the algorithm. In this paper we establish that the matrix associated with Bezout's resultant appearing in the stability test of causal or semicausal recursive filters has 2 as its displacement rank. This permits us to apply the generalized Levinson-Szego algorithm to derive a new algorithm for testing the 2-D digital filters' stability. This algorithm is proposed for quarter-plane or nonsymmetric half-plane recursive filters with real coefficients and without nonessential singularities of the second kind. Its complexity order is equal to 4. Note that the complexity order of the fastest existing algorithms is equal to 5.
引用
收藏
页码:255 / 264
页数:10
相关论文
共 28 条
[1]  
Barret, Benidir, On the optimality of the classical stability criteria for 1-D and 2-D digital recursive filters, Proc. IEEE Internat. Conf. Acoust. Speech Signal Process.-93, Minneapolis, 3, pp. 65-68, (1993)
[2]  
Basu, Fettweis, New results on stable multidimensional polynomials — Part II Discrete case, IEEE Transactions on Circuits and Systems, 23 CAS, 11, pp. 1264-1274, (1987)
[3]  
Benidir, Barret, A Bezout resultant based stability test for 2-D digital recursive filters, Proc. 6th Eur. Signal Processing Conf. EUSIPCO-92, Brussels, Belgium, 2, pp. 989-992, (1992)
[4]  
Benidir, Picinbono, Extensions of the stability criterion for ARMA filters, IEEE Trans. Acoust. Speech Signal Process., 35 ASSP, 4, pp. 425-431, (1987)
[5]  
Bose, Implementation of a new stability test for two-dimensional filters, IEEE Trans. Acoust. Speech Signal Process., 25 ASSP, 2, pp. 117-120, (1977)
[6]  
Bose, Digital Filters Theory and Applications, (1985)
[7]  
Chang, Aggarwal, Design of two-dimensional semicausal recursive filters, IEEE Trans. Circuits and Systems, 25 CAS, 12, pp. 1051-1059, (1978)
[8]  
DeCarlo, Murray, Saeks, Multivariable Nyquist theory, International Journal of Control, 25, 5, pp. 657-675, (1976)
[9]  
Demoment, Equations de Chandrasekhar et algorithmes rapides pour le traitement du signal et des images, Trait. du Sig., 6, 2, pp. 103-115, (1989)
[10]  
Dudgeon, Mersereau, Multidimensional Digital Signal Processing, (1984)