About: Zak transform

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In mathematics, the Zak transform (also known as the Gelfand mapping) 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

Attributes	Values
rdf:type	military conflict
rdfs:label	Zak transform (en)
rdfs:comment	In mathematics, the Zak transform (also known as the Gelfand mapping) 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 (en)
dcterms:subject	Transforms
Wikipage page ID	44778163 (xsd:integer)
Wikipage revision ID	1114393074 (xsd:integer)
Link from a Wikipage to another Wikipage	Complex number Convolution Mathematics Eigenfunction Frequency Signal (electrical engineering) Signal processing Joshua Zak Ceil function Time Exponential function Dilation (affine geometry) Israel Gelfand Transforms Translation (geometry) Discrete Fourier transform Integer Real number Sequence Discrete set Infinite series
sameAs	Zak transform Zak transform Zak transform Zak transform
dbp:wikiPageUsesTemplate	dbt:Reflist
has abstract	In mathematics, the Zak transform (also known as the Gelfand mapping) 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 "Gelfand mapping" because Israel Gelfand introduced it in his work on eigenfunction expansions. The transform was rediscovered independently by Joshua 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 the first to systematically study that transform in a more general setting and recognize its usefulness. (en)
gold:hypernym	Operation
prov:wasDerivedFrom	wikipedia-en:Zak_transform?oldid=1114393074&ns=0
page length (characters) of wiki page	6366 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Zak_transform
is Link from a Wikipage to another Wikipage of	Weil–Brezin Map Z-transform Joshua Zak Israel Gelfand Discrete-time Fourier transform Discrete Fourier transform
is foaf:primaryTopic of	wikipedia-en:Zak_transform

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