Multidimensional sampling: Difference between revisions

Revision as of 19:59, 25 April 2012

Revision as of 21:18, 25 April 2012

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[[File:Moire pattern of bricks small.jpg|thumb|205px|Spatial aliasing in the form of a [[Moiré pattern]].]]

[[File:Moire pattern of bricks.jpg|thumb|205px|Properly sampled image of brick wall.]]

The theorem gives conditions on sampling lattices for perfect reconstruction of the sampled. If the lattices are not fine enough to satisfy the Petersen -Middleton condition, then the field cannot be reconstructed exactly from the samples in general. In this case we say that the samples may be [[Aliasing|aliased]].

A simple illustration of aliasing can be obtained by studying low-resolution images. A gray-scale image can be interpreted as a function in two-dimensional space. An example of aliasing is shown in the images of brick patterns on the right. The top image shows the effects of aliasing when the sampling theorem's condition is not satisfied. If the lattice of pixels is not fine enough for the scene, aliasing occurs as evidenced by the appearance of the [[Moiré pattern]] in the image obtained. The lower image is obtained when a smoothened version of the scene is sampled with the same lattice. In this case the conditions of the theorem are satisfied and no aliasing occurs.