Synthesis of Itˆo Equations for a Shaping Filter with a Given Spectrum

The analytical method for the synthesis of a generator of a random process with a given spectrum in the form of a linear system of Ito’s equations is proposed. The stationarity of a random process is assumed, the spectral and corresponding transfer functions of which are defined in the form of rational fractions. The coefficients of the system of Ito’s equations of the generator are found from recurrent algebraic relations. The method is focused on working with mathematical models of nature random processes, such as the Dryden’s wind model. The transformation of the spectra of the wind gust model in three directions is presented in detail and the corresponding stochastic equations are given.