论文信息 - Groebner basis techniques in multidimensional multirate systems

Groebner basis techniques in multidimensional multirate systems

The Euclidean algorithm is a frequently used tool in the analysis of one-dimensional (1D) multirate systems. This tool is however not available for multidimensional (MD) multirate systems. The authors discus how Groebner basis techniques can fill this gap. After presenting the relevant facts about Groebner bases, they show in a few examples how this technique can contribute to MD multirate systems theory.

Martin Vetterli | Ton Kalker | Hyungju Park

[1] B. Sturmfels,et al. Algorithms for the Quillen-Suslin theorem , 1992 .

[2] Martin Vetterli,et al. Wavelets and filter banks: theory and design , 1992, IEEE Trans. Signal Process..

[3] Sankar Basu,et al. Multidimensional causal, stable, perfect reconstruction filter banks , 1994, Proceedings of 1st International Conference on Image Processing.

[4] B. Buchberger,et al. Grobner Bases : An Algorithmic Method in Polynomial Ideal Theory , 1985 .

[5] P. P. Vaidyanathan,et al. Recent developments in multidimensional multirate systems , 1993, IEEE Trans. Circuits Syst. Video Technol..

[6] H. Park,et al. An Algorithmic Proof of Suslin′s Stability Theorem for Polynomial Rings , 1994, alg-geom/9405003.

[7] David A. Cox,et al. Ideals, Varieties, and Algorithms , 1997 .