Least common right/left multiples of integer matrices and applications to multidimensional multirate systems

The basic building blocks in a multidimensional (MD) multirate system are the decimation matrix and the expansion matrix. These matrices are D×D nonsingular integer matrices, where D is the number of dimensions. The authors show that properties of integer matrices, such as greatest common right/left divisors and right/left coprimeness play important roles in MD multirate systems. They also introduce the concept of least common right/left multiple of integer matrices and derive many useful properties of them. They illustrate the importance of these by applying them to several issues in MD multirate signal processing, including interchangeability of decimators and expanders, delay-chain systems, and periodicity matrices