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TitleParametrized Family of 2-D Non-factorable FIR Lossless Systems and Gröbner Bases
Author(s) Hyungju Park
TypeArticle in Journal
AbstractThe factorability of one-dimensional (1-D) FIR lossless transfer matrices [1] in terms of Givens rotations produces the parameters that can be used for an optimal design of filter banks with prespecified filtering characteristics. Two dimensional (2-D) FIR lossless systems behave quite differently, however. Venkataraman-Levy [2] and Basu-Choi-Chiang [3] have constructed 2-D FIR paraunitary matrices of McMillan degrees (2,2) that are not factorable. Because of the state-space realization used in the construction, they are floating-point approximations, and they do not produce explicit parametrizations that can be used for optimal design process. In this paper, we formulate the lossless condition and nonfactorability condition of a 2-D FIR paraunitary matrix using multivariate polynomials in the coefficients. The resulting polynomial system can be explicitly solved with Gröbner bases. By studying the polynomial system, we obtain a continuous one parameter family of 2-D 2×2 non-factorable paraunitary matrices. As an example, we get a closed-form expression for a 2-D 2×2 paraunitary matrix that is not factorable into rotations and delays.
Keywordslosses, paraunitary, Gröbner bases, non-factorable, parametrization
Length20
ISSN0923-6082
File
URL dx.doi.org/10.1023/A:1011961708408
LanguageEnglish
JournalMultidimensional Syst. Signal Process.
Volume12
Number3-4
Pages345-364
PublisherSpringer Science Business Media B.V.
AddressHingham, MA, USA
Year2001
MonthJuly
Translation No
Refereed No
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