The Zak transform maps a signal of time into a signal that combines both time and frequency information. It is the simplest time-frequency representation of a signal whose value as such is often ignored as a processing tool. Its most usual role is as an intermediary between signal space and a wide range of time-frequency representations, including the ambiguity function, the Wigner distribution, and Weyl-Heisenberg representations.
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- The Zak transform has a long history going back to Gauss’s work on the application of the finite Fourier transform to number theory. In modern times, it was distinguished as an object of study by Zak  and in a slightly different form by Weil , but appears previously in several works as part of derivations.Google Scholar