SU1456955A1 - Device for forming a random process - Google Patents

Abstract

The device relates to the field of computing and can be used to solve a wide range of probabilistic modeling problems. The device contains a random process generator 1, a multiplier 2, a group of 3 multipliers, a group of 4 multiplier, an adder 5, a group of 6 elements

Description

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delays, a group of 7 subtractors, a functional converter 8, a generator of a uniformly distributed random signal 9, a block of 10 comparators and a generator of 11 clock pulses. The purpose of the invention is to improve the accuracy of the device. The goal is achieved through the introduction of new units and functional links. The device allows the formation of a random process with an arbitrary one-dimensional distribution and a given autocorrelation function. 2 Il.

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The invention relates to computing and can be used in solving a wide range of probabilistic modeling tasks.

The aim of the invention is to improve the accuracy of the device.

Figure 1 shows the block diagram of the device; figure 2 - timing diagrams illustrating the operation of the device.

The device contains a random process generator 1, with a one-dimensional distribution function, a multiplier 2, a group of 3 multipliers, a group of 4 multipliers, an adder 5, a group of 6 delay elements, a group of 7 subtractors of a functional converter 8, a generator 9 of a uniformly distributed random signal, a block of 10 comparators and 11 clock pulse generator.

The device works as follows.

The random process generator processes the signal x (t), constant at intervals, 2, ..., where and t is a certain fixed time interval, with the values x (n) x (nAt) 5 and 1.2, uncorrelated and have a uniform distribution in the range corresponding to the segment / 0,1 /.

The generator 9 generates a signal z (t), also constant over the intervals nit ,, 2 ,. .., and taking at these intervals equal values in the range corresponding to the segment / 0.1 /, and the values of z (n) z (nbt),, 2, ..., are uncorrelated with each other, as well as with the values (n),, 2 ....

The comparators block consists of 2K + 1 two-threshold comparators. Comparators trigger thresholds are set

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set of probabilities, Rd.,., R., Pb,, .. Pb - - - -

, P, (Ra, + ... + P, Oh through

the installation inputs of the same name and correspond to the intervals

(0, P), (Ra, Ra, + Ra). (Pfl. Rd + PQ + Pq), etc. The input signals of the comparators a (t), ..., a (t), b (t) ..., b (t), c (t) outside their operation intervals are zero, and within these intervals correspond to one. Thus, the signal а (t) l with probability РД and a (t) 0 with probability 1 - Рд, signal a (t) l with probability РД and a (t) 0 with probability 1 - РО, J etc., and at each moment of time only one of the output signals of this block is equal to one.

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The signals), ..., a (t) are fed to the second inputs of the same names of the group 3, -signals b (t), ..., b (t) to the first inputs of group 4 multipliers, and the signal c (t ). - the second input of the multiplier 2. The first input of the multiplier 2 receives the signal x (t), the first inputs of the multipliers of group 3 receive the output signals from the one-time delay elements of group 6, which are analog sampling-storage devices, and the second inputs of the multipliers Groups 4 of these output signals are received through the calibrators of group 7, each of which performs the conversion.

The signals from the outputs of the multiplier 2 and multipliers of groups 3 and 4 are fed to the input of the adder 5, the output of which U (t) is fed to the input of the first delay element of group 6, as well as to the input of the functional converter 8, carried out (its conversion (U) F - (i) where f (u) inf

yj y: F (yl yj; F is the given distribution function of the random process being formed (if F is a continuous increasing function, then F is the function inverse to F). The output of the functional converter n 8 is the output of the device.

The operation of the generator 1, generator 9 and the delay elements of group 6 sinU (n) a, (n) U (nl) + b, (n) lU (nl) + + b (n) .lU (nK) + c (n) x (n); ,

where a; (n) a (); B; (n) b; (nut); c; (n) c (nut);

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a value of the output signal of the device at the output of the functional converter 8 is equal to

At (t) 9 U (t). . (2) Since for each n in the right-hand side of (1) only one desired is different from zero, then U (n) coincides either with one

y (n) a, (n) y (n-1) + b, (n) (nl) + .... a (n) y (n-K) + “bJn) (nK) + c (n) ); , K + 2, .. ,,

where y (n) y (); Y (n) (n); H) (y) F-l-F (y).

The timing diagram illustrates the operation of the device when, RD Pj, P 1/3, F (y) l-r, y (0) x (0) (figure 2).

With an appropriate choice of MaTpH correlation initial conditions n 1, i..K of equation (2), ensure, R, (m) - (Pa, -Pb,) R (m -) - (Pq, -Pb) R (m- 2) - .. .- () R, (mK) 0; (4) R, (in) - (Pa, Рц) R, (m-2) - (P, -HP) R (m-2) - ...- (Р Р J Ri (mK) 0. ( five)

The autocorrelation function satisfying (4) and (5) corresponds to the spectral density that the random process has, which is the half-sum of two uncorrelated processes formed from white noise using linear K-order filters, one of which has the parameters P -R ,.. . ,, and the other -. RD + P parameters. Therefore, the choice of P values,

R,

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in accordance with b,,,

The R (m) type can be implemented with the help of an 11-clock pulse generator, which generates a sequence of clock pulses Uc with the ut interval.

The values of the signal U (n) U (nAt), p 1,2, ..., at the output of the adder 5 at the same time satisfy the equality

... + a (n) U (n-K) + K-t-2, ..., (1)

with the values U (n-i),, ..., K, either with one of the values l-U (n-i),, ... K, or with x (n). Consequently, if the initial values U (n),, ..., K, have a uniform distribution on the segment / 0,1 /, then the values U (n) also have a uniform distribution on the segment / 0, all n. H & , the output signal of the device y (t), by virtue of (2), has a given distribution function F (y) (1), with

In the broad sense of the process U (n), n-, 2, ..., as well as in the established mode with any initial correlations, the autocorrelation function of the K (n) n process y (n) is equal to

R (m) R, (in) + Rj (m), (3) where the functions R, (w) and K, s (t) are

ry difference equations

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This is based on the standard procedure for the synthesis of forming filters.

Thus, o6pa30Ms, the signal y (t) at the output of the functional converter 8 has a given distribution function F (y) and the required autocorrelation function R (m). g

Claims (1)

Formula invented and A device for forming a random process containing a random process generator with a one-dimensional distribution function, the output of the catapago is connected to the first input of the multiplier, an adder, two groups of multipliers, a group of serially connected delay elements in which the information input of the first element is connected to the output of the adder, the outputs of the delay elements of the group connected to the first inputs of the same multipliers of the first group, the output of the multiplier and the outputs of the multipliers of the first and second groups are connected to the corresponding the inputs of the adder, the generator is uniformly distributed randomly. second signal output to the input koTqpogosoedinen 6jtOKa comparators threshold reference input which are input specifying generated autocorrelation function of a random process, a first group comparator unit outputs connected to second inputs of the multipliers of the first group, second group kosharatbrov soedineia unit outputs with the first Bxo P . pp p . p gp p p Rtlg all) / l; Dami multipliers of the second group, the output of the comparator block is connected to the second input of the multiplier, the generator clock pulses, the output of which is connected to the clock inputs of the delay elements of the group and with the outputs Poll of a random process generator with a one-dimensional distribution function and a generator of a uniformly distributed random signal, about t - l that is, because, in order to increase the accuracy, a group is entered into it subtractors, the inputs of which are connected to the outputs of the same group delay elements, the outputs of the subtractors are connected to the second inputs of the multipliers of the second group, the output of the adder is connected to the input The functional converter is equipped with a String transformation y «F (U), where and is a given distribution function, the output of which is the output of the device. one