Multidimensional probability distributions of the envelope and phase of stationary noise with n0n6aussian statistics

It is shown that there is a unique relationship between the probability distributions of the envelope p(t), the phase ϕ(t), and a quasi-harmonic random process ξ(t) =p(t)cos ψ, $ψ = ω_{о}t+ ϕ(t)$ if ξ, p and ф are stationary. The structure of the distribution functions is obtained. The two-dimensional case is considered in detail. The results are generalized using a model of the quasi-periodic process ξ(t) =p(t)F(ψ), where F(ψ)= F(ψ+2n).