Mutual space-frequency distribution: Analytic calculations of Gaussian signal

Mutual space-frequency distribution is proposed and both the Wigner and Weyl distribution functions are shown to be some particular cases of this distribution. The simple connection is established between the Wigner and Weyl distributions. Mutual distribution of Gaussian signal is analytically obtained. It is shown that the Wigner distribution is formed as the rotational displacement of the Weyl distribution on informational diagram of conjugate coordinates (x;p) on an angle proportional to the mutual parameter t. The results are presented of direct calculations of mutual distribution for Gaussian signal in the mutual domain.