Multidimensional sampling: Difference between revisions

Revision as of 12:16, 8 May 2012

Revision as of 13:21, 8 May 2012

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===Aliasing===

{{main|Aliasing}}

[[Image:Unaliased_sampled_spectrum_in_2D.png|thumb|Fig. 3: Support of the sampled spectrum <math>\hat f_s(.)</math> obtained by hexagonal sampling of a two-dimensional function wavenumber-limited to a circular disc. The blue circle represents the support <math>\Omega</math> of the original wavenumber-limited field, and the green circles represent the repetitions. In this example the discsspectral arerepetitions disjointdo not overlap and hence there is no aliasing. The original spectrum can be exactly recovered from the sampled spectrum.|right|300px]]

[[Image:Aliased_sampled_spectrum_in_2D.png|thumb|Fig. 4: Support of the sampled spectrum <math>\hat f_s(.)</math> obtained by hexagonal sampling of a two-dimensional function wavenumber-limited to a circular disc. In this example, the sampling lattice is not fine enough and hence the discs overlap in the sampled spectrum. Thus the spectrum within <math>\Omega</math> represented by the blue circle cannot be recovered exactly due to the overlap from the repetitions (shown in green), thus leading to aliasing.|right|300px]]

[[File:Moire pattern of bricks small.jpg|thumb|205px|Fig. 5: Spatial aliasing in the form of a [[Moiré pattern]].]]