Mutual space-frequency distribution of Gaussian signal

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