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• Multidimensional_sampling abstract "In digital signal processing, multidimensional sampling is the process of converting a function of a multidimensional variable into a discrete collection of values of the function measured on a discrete set of points. This article presents the basic result due to Petersen and Middleton on conditions for perfectly reconstructing a wavenumber-limited function from its measurements on a discrete lattice of points. This result, also known as the Petersen–Middleton theorem, is a generalization of the Nyquist–Shannon sampling theorem for sampling one-dimensional band-limited functions to higher-dimensional Euclidean spaces.In essence, the Petersen–Middleton theorem shows that a wavenumber-limited function can be perfectly reconstructed from its values on an infinite lattice of points, provided the lattice is fine enough. The theorem provides conditions on the lattice under which perfect reconstruction is possible.As with the Nyquist–Shannon sampling theorem, this theorem also assumes an idealization of any real-world situation, as it only applies to functions that are sampled over an infinitude of points. Perfect reconstruction is mathematically possible for the idealized model but only an approximation for real-world functions and sampling techniques, albeit in practice often a very good one.".
• Multidimensional_sampling thumbnail Hexagonal_sampling_lattice.png?width=300.
• Multidimensional_sampling wikiPageID "35614495".
• Multidimensional_sampling wikiPageLength "15093".
• Multidimensional_sampling wikiPageOutDegree "44".
• Multidimensional_sampling wikiPageRevisionID "679449569".
• Multidimensional_sampling wikiPageWikiLink Aliasing.
• Multidimensional_sampling wikiPageWikiLink B-spline.
• Multidimensional_sampling wikiPageWikiLink Bandlimiting.
• Multidimensional_sampling wikiPageWikiLink Basis_(linear_algebra).
• Multidimensional_sampling wikiPageWikiLink Box_spline.
• Multidimensional_sampling wikiPageWikiLink Brillouin_zone.
• Multidimensional_sampling wikiPageWikiLink Category:Digital_signal_processing.
• Multidimensional_sampling wikiPageWikiLink Category:Multidimensional_signal_processing.
• Multidimensional_sampling wikiPageWikiLink Category:Theorems_in_Fourier_analysis.
• Multidimensional_sampling wikiPageWikiLink Digital_signal_processing.
• Multidimensional_sampling wikiPageWikiLink Discrete-time_Fourier_transform.
• Multidimensional_sampling wikiPageWikiLink Euclidean_space.
• Multidimensional_sampling wikiPageWikiLink File:Aliased_sampled_spectrum_in_2D.png.
• Multidimensional_sampling wikiPageWikiLink File:Hexagonal_sampling_lattice.png.
• Multidimensional_sampling wikiPageWikiLink File:Reciprocal_lattice.png.
• Multidimensional_sampling wikiPageWikiLink File:Unaliased_sampled_spectrum_in_2D.png.
• Multidimensional_sampling wikiPageWikiLink Finite_impulse_response.
• Multidimensional_sampling wikiPageWikiLink Fourier_transform.
• Multidimensional_sampling wikiPageWikiLink Hexagonal_lattice.
• Multidimensional_sampling wikiPageWikiLink Indicator_function.
• Multidimensional_sampling wikiPageWikiLink Inner_product_space.
• Multidimensional_sampling wikiPageWikiLink Interpolation.
• Multidimensional_sampling wikiPageWikiLink Isotropy.
• Multidimensional_sampling wikiPageWikiLink Lanczos_resampling.
• Multidimensional_sampling wikiPageWikiLink Lattice_(group).
• Multidimensional_sampling wikiPageWikiLink Moiré_pattern.
• Multidimensional_sampling wikiPageWikiLink Nyquist–Shannon_sampling_theorem.
• Multidimensional_sampling wikiPageWikiLink Parallelepiped.
• Multidimensional_sampling wikiPageWikiLink Periodic_summation.
• Multidimensional_sampling wikiPageWikiLink Poisson_summation_formula.
• Multidimensional_sampling wikiPageWikiLink Reciprocal_lattice.
• Multidimensional_sampling wikiPageWikiLink Reconstruction_filter.
• Multidimensional_sampling wikiPageWikiLink Sinc_function.
• Multidimensional_sampling wikiPageWikiLink Sphere_packing.
• Multidimensional_sampling wikiPageWikiLink Vector_space.
• Multidimensional_sampling wikiPageWikiLink Wavenumber.
• Multidimensional_sampling wikiPageWikiLink Whittaker–Shannon_interpolation_formula.
• Multidimensional_sampling wikiPageWikiLink Zonohedron.
• Multidimensional_sampling wikiPageWikiLink File:Moire_pattern_of_bricks.jpg.
• Multidimensional_sampling wikiPageWikiLink File:Moire_pattern_of_bricks_small.jpg.
• Multidimensional_sampling wikiPageWikiLinkText "Multidimensional sampling".
• Multidimensional_sampling wikiPageWikiLinkText "multidimensional signal processing".
• Multidimensional_sampling wikiPageWikiLinkText "sampling lattices".
• Multidimensional_sampling wikiPageUsesTemplate Template:DSP.
• Multidimensional_sampling wikiPageUsesTemplate Template:EquationRef.
• Multidimensional_sampling wikiPageUsesTemplate Template:Main.
• Multidimensional_sampling wikiPageUsesTemplate Template:No_footnotes.
• Multidimensional_sampling wikiPageUsesTemplate Template:NumBlk.
• Multidimensional_sampling wikiPageUsesTemplate Template:Reflist.
• Multidimensional_sampling subject Category:Digital_signal_processing.
• Multidimensional_sampling subject Category:Multidimensional_signal_processing.
• Multidimensional_sampling subject Category:Theorems_in_Fourier_analysis.
• Multidimensional_sampling hypernym Process.
• Multidimensional_sampling type Election.
• Multidimensional_sampling type Algorithm.
• Multidimensional_sampling type Theorem.
• Multidimensional_sampling comment "In digital signal processing, multidimensional sampling is the process of converting a function of a multidimensional variable into a discrete collection of values of the function measured on a discrete set of points. This article presents the basic result due to Petersen and Middleton on conditions for perfectly reconstructing a wavenumber-limited function from its measurements on a discrete lattice of points.".
• Multidimensional_sampling label "Multidimensional sampling".
• Multidimensional_sampling sameAs Q6934659.
• Multidimensional_sampling sameAs m.0jkwg5w.
• Multidimensional_sampling sameAs Q6934659.
• Multidimensional_sampling wasDerivedFrom Multidimensional_sampling?oldid=679449569.
• Multidimensional_sampling depiction Hexagonal_sampling_lattice.png.
• Multidimensional_sampling isPrimaryTopicOf Multidimensional_sampling.