Quadratic Fourier transform

In mathematical physics and harmonic analysis, the quadratic Fourier transform is an integral transform that generalizes the fractional Fourier transform, which in turn generalizes the Fourier transform. Roughly speaking, the Fourier transform corresponds to a change of variables from time to frequency (in the context of harmonic analysis) or from position to momentum (in the context of quantum mechanics).

Source: Wikipedia — Quadratic Fourier transform (CC BY-SA 4.0)