Various theoretical issues in multidimensional (m-D) multirate signal processing are formulated and solved. In the problems considered, the decimation matrix and the expansion matrix are nondiagonal, so that extensions of 1-D results are nontrivial. The m-D polyphase implementation technique for rational sampling rate alterations, the perfect reconstruction properties for the m-D delay-chain systems, and the periodicity matrices of decimated m-D signals (both deterministic and statistical) are treated. The discussions are based on several key properties of integer matrices, including greatest common divisors and least common multiples. These properties are reviewed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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Chen et al. (1993) studied this question.
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