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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 wikiPageRevisionID "568620237".
- Multidimensional_sampling hasPhotoCollection Multidimensional_sampling.
- Multidimensional_sampling subject Category:Digital_signal_processing.
- Multidimensional_sampling subject Category:Theorems_in_Fourier_analysis.
- Multidimensional_sampling type Abstraction100002137.
- Multidimensional_sampling type Communication100033020.
- Multidimensional_sampling type Message106598915.
- Multidimensional_sampling type Proposition106750804.
- Multidimensional_sampling type Statement106722453.
- Multidimensional_sampling type Theorem106752293.
- Multidimensional_sampling type TheoremsInFourierAnalysis.
- 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 m.0jkwg5w.
- Multidimensional_sampling sameAs Q6934659.
- Multidimensional_sampling sameAs Q6934659.
- Multidimensional_sampling sameAs Multidimensional_sampling.
- Multidimensional_sampling wasDerivedFrom Multidimensional_sampling?oldid=568620237.
- Multidimensional_sampling depiction Hexagonal_sampling_lattice.png.
- Multidimensional_sampling isPrimaryTopicOf Multidimensional_sampling.
