On General Factorizations for n-D Polynomial Matrices

• Published in: Circuits, systems, and signal processing Vol. 30; no. 3; pp. 553 - 566
• Main Authors: Liu, Jinwang, Li, Dongmei, Wang, Mingsheng
• Format: Journal Article
• Language: English
• Published: Boston SP Birkhäuser Verlag Boston 01.06.2011; Springer Nature B.V
• Subjects: Algorithms; Circuits; Circuits and Systems; Construction; Electrical Engineering; Electronics and Microelectronics; Engineering; Factorization; Instrumentation; Matrix; Polynomial matrices; Polynomials; Signal processing; Signal,Image and Speech Processing; D polynomial matrices; Multidimensional systems; Matrix factorizations; Reduced minors
• ISSN: 0278-081X; 1531-5878
• DOI: 10.1007/s00034-010-9229-x

Multivariate ( n -D) polynomial matrix factorizations are basic research subjects in multidimensional ( n -D) systems and signal processing. In this paper, several results on general matrix factorizations are provided for extracting a matrix factor from a given n -D polynomial matrix whose lower order minors satisfy certain conditions. These results are further generalizations of previous results in (Lin et al. in Circuits Syst. Signal Process. 20(6):601–618, 2001 ). As a consequence, the application range of the constructive algorithm in (Lin et al. in Circuits Syst. Signal Process. 20(6):601–618, 2001 ) has been greatly extended. Three examples are worked out in detail to show the practical value of the proposed method for obtaining general factorizations for a class of n -D polynomial matrices.