IEEE Signal Processing Letters, vol. 4, no. 11, pp. 313-316, Nov. 1997
Designing Commutative Cascades of Multidimensional Upsamplers and Downsamplers
Brian L. Evans
Department of Electrical and Computer Engineering,
Engineering Science Building,
The University of Texas at Austin,
Austin, TX 78712-1084 USA
In multiple dimensions, the cascade of an upsampler by L
and a downsampler by L commutes if and only if the
integer matrices L and M are right coprime and
L M = M L.
This paper 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 = L M-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.
The full paper is available in
Last Updated 11/19/98.