New results in multidimensional multirate systems

In multidimensional multirate systems one encounters an integer matrix M, which typically takes the role of decimators and interpolators. If M is diagonal, many of the concepts of one-dimensional systems extend automatically. In the present work, the author uses the Smith-form diagonalization of M to relate arbitrary systems to systems having diagonal decimation and interpolation matrices. Applications in maximally decimated filter banks and in the study of the generalized DFT (discrete Fourier transform) are considered