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
for and . The Zak transform is sometimes also known
as the Weil-Brezin map.
Brezin, J. "Function Theory on Metabelian Solvmanifolds." J. Funct. Analysis10, 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.
and 
. The Zak transform is sometimes also known
as the Weil-Brezin map.
