ABSTRACT
The Fourier transform analysis can describe the relation between a real signal domain and its spectral domain. The Wigner distribution function (WDF) is a two-dimensional function, which can represent the signal together in the real and frequency domains. The WDF can describe some optical functions, such as the lens effect, the phase modulation, the diffraction grating, the wave propagation, and so on. The four dimensional WDF in the space-time signal is also introduced. The discussion on the transform of the spatio-temporal WDF shows that the transform can be performed by a linear transform of variables. A two variable WDF for the space domain and its frequency domain was defined. In the dispersive media, the Fresnel diffraction and the time-frequency dispersion are caused simultaneously. In the case of the temporal phase modulation, the frequency is changed similarly.
