Synthesis of the main elements of multi-dimensional multi-rate systems. Part I. Nonseparable decimation matrices

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.