SU133622A1 - Stationary random process generator - Google Patents

Description

The invention relates to stationary random process generators containing a memory device, discrete data to continuous converters, a control device and functional converters.

In contrast to the known ones, in the proposed generator, the problem of simulating realizations of a stationary random process is reduced to the well-known problem of generating random variables with predetermined distribution fractions.

The drawing shows a simplified block diagram of the proposed generator.

The generated stationary random process is determined by a step random function.

x (t) a „at t t„ + j; , 1, 2 ... m (1)

Here, / n is a large enough integer; a is the essence of the realization of a random variable A with a c. Average value equal to zero, n with an integral distribution function F (a

r "E tn + - t are realizations of a positive random variable T with an integral distribution function F (t);

t are times.

The correlation function of the stepwise random process x (t} is determined by

where a is the rms value (variance) of the random variable A.

From the properties of the distribution function Φ (t), it follows that Φ (o) 0, and hence from relation (2) we get:

The correlation function (t) that the process should have (this function is set analytically or taken from experiment)

/ (g) (t), (2)

/ (o) (3)

Vo -1: ESP9 i

It is possible to determine the distribution function f (t) using relation (2).

Since the choice of the form of the distribution function P {cC of the random variable A remains free, we can assume that F (a) is a uniform distribution that satisfies condition (3).

A random process gegger generates a static simulation of a given random process by statically simulating random variables A and T.

Under. The static model of the random process defined by the cusp function (1) is understood to be a random process, the correlation function of which coincides with a certain accuracy with / (m).

The proposed generator works as follows.

From the storage device 1, random numbers in the form of discrete signals are transmitted in converting IT 2 and 5 discrete signals into continuous ones. The sipgal from the output of the converter 2 is fed to the functional converter 4, generating a function cp from the signal at the input, the inverse of the distribution function F (t). In device J, the continuous signal is converted into a discrete signal and enters device 6, which controls the output of signals from device 7.

At the output of device 3, a constant continuous signal is maintained until the next discrete signal appears at its input. The signal from device 3 is continuously fed into the instantaneous amplifier 1, which produces a linear function G from the signal at the input, the inverse function 1 and distribution P (a. The signals at the output of amplifier 7 are realizations of the stationary random process defined by the step function (1).

A set of functions P) and f is produced on the commutator {011 generator panel.

Subject and s about b) e te and

The ieriepaTop of stationary random processes that contains a memory device, discrete data to continuous converters, a control device and functional converters, characterized in that, in order to obtain realizations of a random process, a memory device for random numbers is connected through discrete value converters non-continuous with functional converters serving for a set of functions that are inverse with respect to the numerical functions of the distribution of random variables.