The role of Smith-form decomposition of integer-matrices, in multidimensional multirate systems

Multirate topics such as decimation, interpolation, polyphase decomposition, and filter bank theory have been extended in the past for the case of multidimensional systems. It is pointed out that the decimation matrix plays a crucial role in these extensions. Unless the matrix is diagonal, separable techniques cannot be used either for theoretical derivations or practical implementations. In this context, the author introduces a diagonalization technique for the decimation matrix, which brings the results closer to the separable (hence one-dimensional) case