Title :
Designing commutative cascades of multidimensional upsamplers and downsamplers
Author_Institution :
Dept. of Electr. & Comput. Eng., Texas Univ., Austin, TX, USA
Abstract :
In multiple dimensions, the cascade of an upsampler by L and a downsampler by M commutes if and only if the integer matrices L and M are right coprime and LM=ML. This letter presents algorithms to design L and M that yield commutative upsampler/dowsampler cascades. We prove that commutativity is possible if the Jordan canonical form of the rational (resampling) matrix R=LM/sup -1/ is equivalent to the Smith-McMillan form of R. A necessary condition for this equivalence is that R has an eigendecomposition and the eigenvalues are rational.
Keywords :
eigenvalues and eigenfunctions; matrix decomposition; signal sampling; Jordan canonical form; commutative cascades design; eigendecomposition; integer matrices; multidimensional downsamplers; multidimensional upsamplers; rational eigenvalues; rational matrix; resampling matrix; right coprime matrices; Algorithm design and analysis; Audio tapes; Eigenvalues and eigenfunctions; Filtering; Filters; Interpolation; Matrix decomposition; Multidimensional systems; Sampling methods; Signal processing algorithms;
Journal_Title :
Signal Processing Letters, IEEE
