Muestreo y reconstrucción de realizaciones de la suma de dos procesos Gaussianos

Abstract

Resumen. Con base en la regla de la esperanza matemática condicional se investiga el procedimiento de muestreo-reconstrucción para la suma de dos procesos Gaussianos. También se estudian las funciones básicas y la función de error de reconstrucción, cuando el número de muestras y la longitud del intervalo de muestreo son arbitrarios.

Two-Dimensional Sampling-Recovery Algorithm of a Realization of Gaussian Processes on the Input and Output of Linear Systems

“…Comparison of the curves in Figure 4 and Figure 7 shows that the maximum error values differ significantly. This fact is explained by the greater smoothness of the studied processes in this example compared to the processes in Section 5.1 Example 1 (see more about this effect in [ 13 , 14 , 16 ]). In addition, note that the curve 1 is asymmetric compared to curve 3.…”

“…As in the one-dimensional case [ 13 , 14 , 15 , 16 ], based on (10), we introduce the definition of a multidimensional basic function …”

“…There is a small smoothed minimum at the highs of curve 2 in the middle of the total interval. This effect for non-Markov processes is described in the analysis of a one-dimensional algorithm [ 13 , 14 , 16 ]. In this example, the difference in the maxima of the one-dimensional curves is insignificant.…”

“…The application of the CMM (see, for example, [ 10 , 11 , 12 ]) to the study of SRA of realizations of random processes has a number of advantages (see [ 13 , 14 , 15 , 16 , 17 ] and references therein) in comparison with the well-known Balakrishnan theorem (TB) [ 18 ] and many of its generalizations. Indeed, SRA based on CMM are distinguished by such positive qualities as: (1) Restoration of a sampled realization of a random process according to the CMM automatically provides a minimum of the root-mean-square error of restoration; (2) the restoring function, like the restoring error function in the general case, takes into account the main statistical characteristics of a random process: Probability density, covariance, and cumulant functions; spectrum (a process with a limited spectrum is a special case); (3) the considered algorithms are optimal for any number and location of samples (the variant of periodic samples is a special case); (4) general analytical expressions for the considered SRA cover stationary and non-stationary variants of stochastic processes; (5) sampled stochastic processes can be Gaussian and non-Gaussian, continuous and discontinuous, etc.…”

Model of Random Field with Piece-Constant Values and Sampling-Restoration Algorithm of Its Realizations

“…The conditional mean recovery algorithm automatically provides the minimum mean square recovery error. Numerous examples of the application of the discussed technique can be found in [18][19][20][21]. In particular, on the basis of this method were analyzed the realizations of the SRA binary Markov process [22] and the realizations of the SRA of a piecewise continuous Markov process with an arbitrary number of states [23].…”