Details:
Title  Parametrized Family of 2D Nonfactorable FIR Lossless Systems and Gröbner Bases  Author(s)  Hyungju Park  Type  Article in Journal  Abstract  The factorability of onedimensional (1D) 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 (2D) FIR lossless systems behave quite differently, however. VenkataramanLevy [2] and BasuChoiChiang [3] have constructed 2D FIR paraunitary matrices of McMillan degrees (2,2) that are not factorable. Because of the statespace realization used in the construction, they are floatingpoint 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 2D 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 2D 2×2 nonfactorable paraunitary matrices. As an example, we get a closedform expression for a 2D 2×2 paraunitary matrix that is not factorable into rotations and delays.  Keywords  losses, paraunitary, Gröbner bases, nonfactorable, parametrization  Length  20  ISSN  09236082 
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 URL 
dx.doi.org/10.1023/A:1011961708408 
Language  English  Journal  Multidimensional Syst. Signal Process.  Volume  12  Number  34  Pages  345364  Publisher  Springer Science Business Media B.V.  Address  Hingham, MA, USA  Year  2001  Month  July  Translation 
No  Refereed 
No 
