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Zak Transform


The Zak transform is a signal transform relevant to time-continuous signals sampled at a uniform rate and an arbitrary clock phase (Janssen 1988). The Zak transform of a signal can be considered as a mixed time-frequency representation of f

 (Zf)_T(t,nu)=T^(1/2)sum_(k=-infty)^inftyf(t+kT)e^(-2piiknuT)

for 0<=t<=T and 0<=nu<=T^(-1). The Zak transform is sometimes also known as the Weil-Brezin map.


This entry contributed by Ronald M. Aarts

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References

Brezin, J. "Function Theory on Metabelian Solvmanifolds." J. Funct. Analysis 10, 33-51, 1972.Janssen, A. J. E. M. "The Zak Transform: A Signal Transform for Sampled Time-Continuous Signals." Philips J. Res. 43, 23-69, 1988.Weil, A. "Sur certains groupes d'opérateurs unitaires." Acta Math. 111, 143-211, 1964.Zak, J. "Finite Translations in Solid-State Physics." Phys. Rev. Lett. 19, 1385-1387, 1967.Zak, J. "Dynamics of Electrons in Solids in External Fields." Phys. Rev. 168, 686-695, 1968.

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Zak Transform

Cite this as:

Aarts, Ronald M. "Zak Transform." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ZakTransform.html

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