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- Zak_transform abstract "In mathematics, the Zak transform is a certain operation which takes as input a function of one variable and produces as output a function of two variables. The output function is called the Zak transform of the input function. The transform is defined as an infinite series in which each term is a product of a dilation of a translation by an integer of the function and an exponential function. In applications of Zak transform to signal processing the input function represents a signal and the transform will be a mixed time–frequency representation of the signal. The signal may be real valued or complex-valued, defined on a continuous set (for example, the real numbers) or a discrete set (for example, the integers or a finite subset of integers). The Zak transform is a generalization of the discrete Fourier transform.The Zak transform had been discovered by several people in different fields and was called by different names. It was called the "Gel'fand mapping" because I.M. Gel'fand introduced it in his work on eigenfunction expansions. The transform was rediscovered independently by J. Zak in 1967 who called it the "k-q representation". There seems to be a general consent among experts in the field to call it the Zak transform, since Zak was indeed the first to systematically study that transform in a more general setting and recognize its usefulness.".
- Zak_transform wikiPageID "44778163".
- Zak_transform wikiPageLength "6383".
- Zak_transform wikiPageOutDegree "19".
- Zak_transform wikiPageRevisionID "678865442".
- Zak_transform wikiPageWikiLink Category:Transforms.
- Zak_transform wikiPageWikiLink Ceil_function.
- Zak_transform wikiPageWikiLink Complex_number.
- Zak_transform wikiPageWikiLink Convolution.
- Zak_transform wikiPageWikiLink Dilation_(affine_geometry).
- Zak_transform wikiPageWikiLink Discrete_Fourier_transform.
- Zak_transform wikiPageWikiLink Discrete_set.
- Zak_transform wikiPageWikiLink Eigenfunction.
- Zak_transform wikiPageWikiLink Exponential_function.
- Zak_transform wikiPageWikiLink Floor_and_ceiling_functions.
- Zak_transform wikiPageWikiLink Frequency.
- Zak_transform wikiPageWikiLink Homothetic_transformation.
- Zak_transform wikiPageWikiLink I.M._Gelfand.
- Zak_transform wikiPageWikiLink Infinite_series.
- Zak_transform wikiPageWikiLink Integer.
- Zak_transform wikiPageWikiLink Isolated_point.
- Zak_transform wikiPageWikiLink Israel_Gelfand.
- Zak_transform wikiPageWikiLink Mathematics.
- Zak_transform wikiPageWikiLink Real_number.
- Zak_transform wikiPageWikiLink Series_(mathematics).
- Zak_transform wikiPageWikiLink Signal_(electrical_engineering).
- Zak_transform wikiPageWikiLink Signal_processing.
- Zak_transform wikiPageWikiLink Time.
- Zak_transform wikiPageWikiLink Translation_(geometry).
- Zak_transform wikiPageWikiLinkText "Zak transform".
- Zak_transform hasPhotoCollection Zak_transform.
- Zak_transform wikiPageUsesTemplate Template:Reflist.
- Zak_transform subject Category:Transforms.
- Zak_transform hypernym Operation.
- Zak_transform type MilitaryConflict.
- Zak_transform comment "In mathematics, the Zak transform is a certain operation which takes as input a function of one variable and produces as output a function of two variables. The output function is called the Zak transform of the input function. The transform is defined as an infinite series in which each term is a product of a dilation of a translation by an integer of the function and an exponential function.".
- Zak_transform label "Zak transform".
- Zak_transform sameAs m.012hdsr9.
- Zak_transform wasDerivedFrom Zak_transform?oldid=678865442.
- Zak_transform isPrimaryTopicOf Zak_transform.