The authors review the fundamentals of multidimensional (M-D) multirate signal processing and present recent and new developments in M-D multirate systems. A method is presented for deriving all parallelepiped-shaped filters in M-D multirate applications from an appropriate 1-D filter. It is shown that the generalized-pseudocirculant property is necessary and sufficient for an M-D maximally decimated filter-bank system to be free from aliasing. It is shown how the Smith form, Smith-McMillan form, and the least common multiples of integer matrices can resolve many nonseparable M-D multirate problems. The condition for alias-free decimation and the multistage design of decimation systems are mentioned.
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