The basic form of Heisenberg's uncertainty principle can be derived by considering the change in the standard deviation of a Gaussian after being transformed by this function.
The 4F correlator is used in a field of optics that commonly employs this transformation, because the field radiated by a planar object is related by it to its point source. The power spectral density is related to the autocorrelation by this function according to the Wiener-Khinchin theorem. The Wigner-Seitz cell around the origin of a space defined as this function of the real space is known as the Brillouin zone; that space is known as (*) reciprocal space. The basic form of Heisenberg's uncertainty principle can be derived by considering the change in the standard deviation of a Gaussian after being transformed by this function. A wavefunction can be transformed from position- to momentum-space by this function. For 10 points, name this integral transform which takes functions from the time domain to the frequency domain.
The 4F correlator is used in a field of optics that commonly employs this transformation, because the field radiated by a planar object is related by it to its point source.
Fourier transform [do not accept “discrete Fourier transform” or “discrete-time Fourier transform”]