Geodesic
Synthesis of the main elements of multi-dimensional multi-rate systems. Part~I. Nonseparable decimation matrices
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 11 (2008) no. 1, pp. 95-113.

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A synthesis method for multi-dimensional decimation matrices is developed for a given number of channels and dimension. Decimation matrices are used in multi-dimensional multi-rate systems. The method is based on application of eigenvalues techniques and the Groebner bases. A full parametrization of decimation matrices is given for two-and three-dimensional cases. Peculiarities of the four-dimensional case are considered. 
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M. K. Tchobanou. Synthesis of the main elements of multi-dimensional multi-rate systems. Part~I. Nonseparable decimation matrices. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 11 (2008) no. 1, pp. 95-113. http://geodesic.mathdoc.fr/item/SJVM_2008_11_1_a7/

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