DocumentCode
1256938
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
Volume
37
Issue
3
fYear
1991
fDate
5/1/1991 12:00:00 AM
Firstpage
695
Lastpage
698
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;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/18.79936
Filename
79936
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