Distribution (mathematics)

Fractional Fourier transform

Mathematics

Fourier analysis

Sine and cosine transforms

Mathematical analysis

Discrete Fourier transform (general)

Fourier transform

Symmetry

We show, in a formal way, how a class of complex quasiprobability distribution functions may be introduced by using the fractional Fourier transform. This leads to the Fresnel transform of a characteristic function instead of the usual Fourier transform. We end the manuscript by showing a way in which the distribution we are introducing may be reconstructed by using atom-field interactions.

Quasiprobability Distribution Functions from Fractional Fourier Transforms