Factorization of M-D Polynomial Matrices for Design of M-D Multirate Systems
نویسندگان
چکیده
The problem of the design of effective 2-D and 3-D multirate systems with prescribed properties is considered using tools from commutative algebra. Results for factoring 2-channel polyphase matrices are presented. After such a factorization, the number of computations may be reduced. For a 3-channel multirate system, an algorithmic version of Suslin’s stability theorem may be useful for factoring the polyphase matrices.
منابع مشابه
On nest modules of matrices over division rings
Let $ m , n in mathbb{N}$, $D$ be a division ring, and $M_{m times n}(D)$ denote the bimodule of all $m times n$ matrices with entries from $D$. First, we characterize one-sided submodules of $M_{m times n}(D)$ in terms of left row reduced echelon or right column reduced echelon matrices with entries from $D$. Next, we introduce the notion of a nest module of matrices with entries from $D$. We ...
متن کاملThe role of integer matrices in multidimensional multirate systems
The basic building blocks in a multidimensional (MD) multirate system are the decimation matrix M and the expansion matrix L. For the D-dimensional case these a re D X D nonsingular integer matrices. When these matrices a re diagonal, most of the one-dimensional (ID) results can be extended automatically. However, for the nondiagonal case, these extensions are nontrivial. Some of these extensio...
متن کاملRecent developments in multidimensional multirate systems
Multidimensional (MD) multirake systems, which find applications in the coding and compression of image and video data, have recently attracted much attention. The basic building blocks in an MD multirate system itre the decimation matrix M, the expansion matrix L, and MD digital filters. With D denoting the number of dimensions, M :and L are D X D nonsingular integer matrices. When these matri...
متن کاملTHE USE OF SEMI INHERITED LU FACTORIZATION OF MATRICES IN INTERPOLATION OF DATA
The polynomial interpolation in one dimensional space R is an important method to approximate the functions. The Lagrange and Newton methods are two well known types of interpolations. In this work, we describe the semi inherited interpolation for approximating the values of a function. In this case, the interpolation matrix has the semi inherited LU factorization.
متن کاملNew Bases for Polynomial-Based Spaces
Since it is well-known that the Vandermonde matrix is ill-conditioned, while the interpolation itself is not unstable in function space, this paper surveys the choices of other new bases. These bases are data-dependent and are categorized into discretely l2-orthonormal and continuously L2-orthonormal bases. The first one construct a unitary Gramian matrix in the space l2(X) while the late...
متن کامل