Digital complex statistical analysis based on sign-function representation of random processes

The concept of complex operative definition of characteristics of stationary random processes is considered in article. The basis of this concept is formalized description of a measurement of the probability characteristics by using generalized equation of statistical measurements. The algorithm for estimating any probability characteristics is considered as a set of interrelated basic measurement and computational transformations. Special attention is paid to the primary digital transformation of a random process. The conversion to digital form is considered as the most important stage of statistical measurement that determines the efficiency of digital processing of the received data and the organization of complex measurements. Sign-function analog-stochastic quantization is proposed to use as a standardized primary transformation of random processes in digital form. This type of quantization based on the use of random auxiliary signals which perform the function of stochastic quantization threshold. The result model of the sign-function analog-stochastic quantization obtained on the basis of the theory of discrete-event simulation. Using sign-function stochastic quantization has allowed realizing an approach that allows the analytical calculation of the operators of integration in the development of digital algorithms for estimating probabilistic characteristics. We described the development of fast digital algorithms for computing estimates of the correlation and cross-correlation functions. Also presents the development of numerical algorithm for the calculation of power spectral density. A unified approach to algorithm design ensures homogeneous structure and informational, programming and metrological compatibility. This opens up the possibility of integration of these algorithms for rapid statistical analysis of random processes.