The commutativity of up/downsampling in two dimensions
- 1 May 1991
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 37 (3) , 695-698
- https://doi.org/10.1109/18.79936
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
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