Title :
The commutativity of up/downsampling in two dimensions
Author :
Kovacevic, Jelena ; Vetterli, Martin
Author_Institution :
Dept. of Electr. Eng., Columbia Univ., New York, NY, USA
fDate :
5/1/1991 12:00:00 AM
Abstract :
The authors state and prove a theorem solving the problem of commutativity in two dimensions. It is shown under which conditions upsampling and downsampling can be interchanged in two dimensions. This is the generalization to arbitrary two-dimensional lattices of the result that one-dimensional upsampling and downsampling commute if and only if their sampling rates are coprime. Some illustrative examples are given. The result holds for arbitrary sampling lattices.
Keywords :
filtering and prediction theory; information theory; arbitrary two-dimensional lattices; commutativity; downsampling; filter banks; sampling rates; two dimensions; upsampling; Buildings; Commutation; Design methodology; Filter bank; Lattices; Machine learning; Multidimensional systems; Polynomials; Sampling methods; Vectors;
Journal_Title :
Information Theory, IEEE Transactions on
