SU1251119A2 - Device for measuring frequency distribution function - Google Patents

Abstract

The invention relates to computing and measurement technology and can be used in the study of the static characteristics of continuous random processes and is an improvement of the device along. No. 390536. The purpose of the invention is an extension of the class of problems to be solved. For this, the device along a.s. No. 390536 additionally introduced a comparison circuit, three delay elements, a trigger, an amplitude-pulse modulator, an amplitude selector, four electronic keys, six switches, a push-button switch. By measuring statistical characteristics that distinguish the uninterrupted Markov process from the non-Markov process, the class of solved problems is expanded. 1 il. ts5 pr rsj

Description

The invention relates to measurement and computing technology, can be used in determining the statistical characteristics of random processes, and is an improvement in the device. No. 390536.

The purpose of the invention is to expand the class of tasks to be solved by measuring the conditional probability density of the form aaw x () fx (t), x (t-t :), and also functionI.

tion

(tt; :) U (t), x (t-t) l ()

by means of which it is possible to distinguish the one-dimensional Markov process from the non-Markov process, and also reasonably choose mathematical models for describing real processes.

The drawing shows a functional diagram of an apparatus for measuring probability density.

The device contains the first input 1 of the first pulse-amplitude modulator (AIM) 2, the first amplitude selector 3, the first element I. 4, the counter 5, the second element And 6, the divider frequency 7, the first trigger 8, the first push button switch 9, the second switch 10 with stationary contacts 11 and 12, a GZ pulse generator, a third element AND 14, a first comparison circuit 15, a voltage source 16, a second device output 17, a second 18 and a third 19 trigger, a fourth 20 and fifth 21 And elements, the first element 22 delays, element OR 23, fifth switch 24 with fixed ontact 25 - 27; the first switch 28 with fixed contacts 29 and 30, the third switch 31 with fixed contacts 32 and 33, the fourth switch 34 with fixed contacts 35 and 36, the first key 37, the second pulse-amplitude modulator (AIM) 38, the second delay element 39, the second comparison circuit 40, the second key 41, the second amplitude selector 42, the third delay element 43, the fourth trigger 44, the third 45 and the fourth 46 keys, the fourth delay element 47, the second additional switch 48 with fixed contacts. 49 and 50, the fourth additional switch 5 with fixed contacts 52 and 53,

with

about

five

-

20

25

thirty

35

40

45

50

55

the third additional switch 54 with fixed contacts 55 and 56, the fifth additional switch Blade 57 with fixed contacts 58 - 60, the first additional switch 61 with fixed contacts 62 and 63, the sixth additional switch 64 with fixed contacts 65 and 66, the second push button switch 67. The numbers of moving contacts of the switches coincide with the numbers of the switches.

The first input of the device 1 is connected to the information input of the first AIM 2, the output of which through the first amplitude selector 3 is connected to the first input of the first element I 4 and also to the first fixed contact 30 of the first switch 28. The output of the first element I 4 is connected to the information input of the counter 5 The first input of the second element And 6 is connected to the movable contact 28 of the first switch, its second input is connected to the output of the first trigger 8, to the second fixed contact 33 of the third switch 31, to the second input of the first element And 4, to the second fixed contact 36 of the fourth switch 34, as well as to the first input of the third element And 14, the output of the second element And 6 through frequency divider 7 is connected to the first input of the first trigger 8, as well as to the control input of the counter 5. Generator 13 pulses through the movable 10 and the first fixed contact 11 of the second switch is connected to the first fixed contact 29 of the first switch, to the third fixed contact of the fifth switch, through the first push button switch to the second input of the first trigger 8, through the normally open contacts of the second push-button switch with the first input of the fourth trigger 44. Through the movable contact 10 and the stationary contact

12 second generator switch

13 pulses are connected to the second fixed contact 26 of the fifth switch, to the output of the third element I 14, to the third fixed contact: the tact of the 60th fifth additional switch, to the second input of the third key 45, to the second input of the fourth key 46, to the second fixed contact 53 the fourth additional switch 51, in addition, the pulse generator 13 is directly connected to the second fixed contact 56 of the third additional switch 54. The second input 17 of the device through the movable 61 and the second fixed 63 end the cycles of the first additional switch are connected to the second input of the first comparison circuit 15, the output of which is connected to the second input of the third element AND 14, with the moving contact 64 of the sixth additional switch, and also with the output of the second amplitude selector 42. The first input of the first comparison circuit 15 connected to the output of the voltage source 16. The second device input 17 through the movable 61 and the first stationary 62 contacts of the first additional switch is connected to the first inputs of the first key 37, the second AIM 38, the second circuit we have 40 comparisons, as well as fixed contacts 50 of the second additional switch 48. The output of the first switch 37 is connected to the second input of the first comparison circuit 15, the output of the second AIM 38 is connected to the input of the second amplitude selector 42. The additional output of the voltage non-voltage 16 through the control input and the output of the second key 41 is connected to the second input of the second comparison circuit 40, the output of which through the second delay element.39 is connected to the second input of the second AIM 38. The fixed contact 65 of the sixth additional switch is via The delay element 43 is connected to the second input of the fourth flip-flop 44, as well as through normally closed Trie contacts of the second push-button switch to the first input of the fourth flip-flop 44. The single output of the fourth flip-flop 44 is connected to the information inputs of the second 41 and third 45 keys, and zero its output is connected to the control inputs of the first 37 and fourth 46 keys. The outputs of the third 45 and fourth 46 keys are connected to the first. fixed contacts 52 and 55 of the fourth and third additional switches, respectively. The first input 1 of the device is connected to the movable contact 48 of the second additional switch. Moving contact 54 of the third optional

the switch is connected to the first input of the first Element And 21 and to the second input of the second trigger 18. The movable contact 5 of the fourth additional switch is connected to the first input of the third trigger 19, as well as to the first input of the fourth And 20 element, the output of which through the first delay element 22 is connected to the second input of the element OR 23 and to the first input of the second trigger 18. The output of the fifth element And 21 is connected to the movable contact of the 57th fifth additional switch, to the second input of the third trigger 19 and through the fourth element 47 delays with the first fixed contact 58 of the fifth additional switch and with the first input of the element OR 23. The output of the element 23 through 23 the first fixed 25 and the movable 24 contacts of the fifth switch are connected to the control input of the first AIM 2. The output of the second trigger 18 is connected to the second input of the fourth element And 20, as well as through the first fixed 32 and the movable 31 contacts of the third switch with the third input of the first element And 4. The output of the third trigger 19 is connected to the second input of the fifth element And 21, and also through the first odvizhny 35 and fourth movable contacts of the switch 34 to a third input of the second AND gate 6.

The dp probability density measurement device operates in various modes as follows.

1. Measurement of unconditional density w / y /.

The instrument measures the unconditional probability density from / y / when the following contacts are connected in the jumpers: 24 and 27, 28 and 29, 31 and 33, 34 and 36, 10 and 11, 48 and 49, 51 and 53, 54, 56, 57 and 58, 61-, and 63, 64 and 66.

The voltage y is supplied through the input 1 to the input of the first AIM 2, to the gating input of which pulses of the generator of 13 pulses (selections) are applied. The output pulses of the AMI 2, whose amplitudes are proportional to the values of the implementation voltage at the moments of arrival of sampling pulses, are fed to an amplitude selector 3, where the analysis level y and the width of the differential corridor A y are set. During the interval

measurements, determined by the presence of the resolving potential at contacts 32 and 33, the pulses appearing at the output of the amplitude selector 3 pass to the counter 5. The number A counted by the counter 5, related to the number of samples N over the measurement interval and the width of the differential corridor, gives an estimate of the density of distribution

0), -1- Lou

BUT

N

The number of samples N is equal to the recalculation factor of frequency divider 7, when N 10 (/ y, counter 5 (pulses) at the end of the measurement interval is an estimate:

wV

 A - 10

where q is an integer that defines the position of a comma in indication A.

2. Measurement of conditional density of distribution with (y / x).

If switches 24, 28, 31, 34, and 10 are closed at contacts 26, 29, 33, 36, and 12, respectively, and the remaining switches remain in the same position, then the device measures the conditional probability density distribution and (y / x).

The implementation voltage y / t / of the random process Y / t / is supplied to the first input of device 1, and the voltage of the realization x / t / of the random process X / i /, which is permanently connected to the test, is fed through the second input 17 and contacts 61- 63 of the first additional switch to the second input of the first circuit 15 of the comparison. The first input of this circuit comes from a voltage source 16, relative to which the conditional probability density is determined. When the condition is satisfied, the output of the first comparison circuit 15 is a pulse that flows through the third element 14 (if there is at its second input, the permitting voltage) to the gate input of the first PAM 2. Those of the pulses formed during the sampling moments at its output that fell into the differential corridor of the amplitude selector 3 arrive through the first element 4, while it is open, into counter 5 .E whether the measurement condition for the interval x / t / X vtoln is N times, i.e., the total number of samples is N, and in the counter 5 is recorded B pulses, then the estimate of the conditional probability density distribution is expressed by the formula:

to

 , 1B

 Y / x --- --jj-.

Since the coefficient of recalculation of the divider 7 frequency C 10/4 y and C N, the estimate of the conditional density is determined by the relation:

r1

with a / x B 10

3. Measurement fztaktsii kolligatsii

1 (t).

To directly measure the collision function, i.e. an attitude

.. G)) / xCt) -x

) -.

the switches 24, 28, 31, 34 and 10 are set to the positions indicated in the diagram, i.e. respectively, they are closed on contacts 25, 30, 32, 35, and 11. At the same time, the remaining five switches remain in the same positions. The voltages of the realizations y / t / and x / t / are fed to inputs 1 and 17.

Prior to the start of the circuit, the second 18 and third 19 triggers are in the zero position and at the second inputs of the fourth 20 and fifth 21 I elements are the inhibitory potentials. When the generator of 13 pulses begins to work, its impulse throws the second trigger 18 into a single position. The fourth element And 20 prepared for the transmission of pulses that can come from the output of the third element And 14, and the first element And 4 - to the transmission of the output pulses of the amplitude selector 3.

After pressing the push-button switch 9, the first pulse of the geyerator 13 pulses flips trigger 8 to the single position and the first voltage goes to the first 4, second 6 and third 14 elements And. From this point on, it is possible to transfer the output pulses of the amplitude selector 3 to the counter 5 (pulses) through the first AND 4 element (if

at its second input there is a permit voltage from the second trigger I8) or to a frequency divider 7 through the second element 6 (if the permit voltage is supplied from the output of the third trigger 19). In addition, the third element 14 is unlocked. The first impulse, appearing at the output of the first comparison circuit 15, when the condition {{/ X) is satisfied, passes through the third element 14 and, having thrown the third trigger 19 into a single position, is fed through the fourth element I 20, the first delay element 22, the OR element 23, and contacts 25-24 to the gate input of the first AIM 2. If the output pulse AIIM 2, whose amplitude is proportional to (i +, falls into the differential corridor U of the amplitude selector 3, then It is transmitted through the first element AND 4 to the counter 5. Impulse Having appeared at the output of the first delay element 22, it flips the second trigger 18, returning it to the zero position. While this position remains, the output pulses of the third element And 14 cannot pass through the fourth element And 20, since the second trigger 18 in the zero position, and the third trigger 19 - in the unit, the first element And 4 is locked, and the second element And 6 open.

The next pulse of the generator 13 pulses in parallel is fed to the input of the second trigger 18, sending it to the single position, and to the first input of the fifth element I 21, Since this element is open (the third trigger 19 in the single position), the pulse passes through it , the element OR 23 and contacts 25-24 to the gate input ASh 2. In addition, it enters the input of the third trigger 19 and returns it to the zero position, which makes it impossible to further transmit pulses of the generator 13 pulses (samples) through the fifth element And 21 until the moment eye not Vits pulse at the output of the first comparing circuit 15, which again will transfer third flip-flop 19 in a single position.

The output pulse of the first AIW 2, provided that its amplitude, proportional to the voltage of the realization y / 1 / at the moment of arrival of the strobing pulse on the AIM 2, will be

5 0 5 20, 25 30 35 0 5

5I1I98

inside di (1) Fere (P1ip, pnogo corridor, passes through open the second element And 6 in the frequency divider 7.

Thus, LIM 2 is alternately gated between the output and my memory of the first comparison circuit 15 (conditional distribution sample), then the pulse generator of 13 pulses unconditional distribution sample). This means that the number of conditional and unconditional distributions carried out during the analysis of the sample are the same and equal to N

If during the analysis interval when building the AIM 2 pulses, from the first comparison circuit 15, B pulses appear (out of the total number of N samples) at the output of the amplitude selector 3, and A pulses occur when gating with the pulse generator signals 13, then ratios (collision functions) L (with V / A. Since the analysis continues until the scaling circuit of the frequency divider 7 overflows, then, by setting the scaling factor 10, we determine the duration of the analysis until the frequency divider 7 receives 10 pulses. T When the estimate is determined from the formula -XB.

Since it is more convenient to use the advanced collie function -) (.) 1, the device provides for recording in the counter 5 pulses of the number 10 in the return code. This operation is carried out by the output pulse of frequency divider 7.

4. Measurement of conditional distribution density

(t + c:) / x (t), x (t- c:) l.

The dp measurements of the conditional density of the form (t +) / X Ct), x (tT) in the switches must be closed contacts 28 and 29, 10 and 12, 31 and 33, 34 and 36, 25 and 24, 48 and 50, 51 and 52 , 54 and 55, 57 and 60, 61 and 62, 64 and 66, Realization of the random process x / t / under investigation through any of the inputs of the device enters the first inputs of the first key 37, the second AIM 38 and the second comparison circuit 40. By pressing the button 67, the fourth trigger 44 is set to such a state that the second 41 and third 45 keys are open, and the first 37 and fourth 46 are closed.

9, 1

From the additional output of voltage source I6, through the open second key 41, a threshold value x is set in the second comparison circuit 40. When the voltage of the implementation x / i / at time i; exceeds the threshold x at the output of the second comparison circuit 40 a pulse is generated, which after a delay of time T in the second delay element 39 arrives at the second input of the second modulator 38. At the same time, a count x (tj + t) is generated at its output the input of the second amplitude selector 42, in which the level x is set, and the width of the differential corridor Ax ,. If the counting x (–t; + T) falls into the corridor & x ,, then the pulse at time ij –f T passes through the third element 14 and pins 60 and 57 of the additional switch to the input of the fourth delay element 47. After a time delay with a pulse, the element OR 23 and the contacts 25 and 24 of the fifth switch pass, at time i; + + T + f strobe first AIM 2, the output of which produces a count of the implementation x (-t; + T + 2). This count goes to the first amplitude selector 3, in which the analysis level x and the width of the differential corridor i X are set If the count x (i, - T) falls into their differential corridor, then it goes through the first element I 3 and is recorded by the counter 5. Obviously, the count x (–t; + T + () may not pass through the first amplitude selector 2 regardless of this, the impulse from the output of the third element I 14 at the time t; + T through the contacts 12 and 10 of the second switch, contact You are 29 and 28 of the first switch and the second element of AND 6 is fed to the input of the frequency divider 7. Since the count x (t; + T) is with reference to the count X (;) X. ,, and X {{, , + T; X, then the ratio of the number of readings of the counter 5 li frequency divider 7 gives an estimate of the value of the conditional density of the distribution

(t, 4-T + t) / x (t; bif2, x (),

for selected levels of analysis. Given the stationarity of the process under study, this estimate will coincide with the estimate of the conditional density of the form

with x (t i t) / X Ct). ,, X t-t x g dl selected

5 5 0 5 0 5 0

five

9K)

levels of analysis x, x, x ,. Mening level X with fixed x ,, x, we obtain a set of estimates of the desired density. Changing the delay time T, the measurement results show how the type of conditional distribution changes at the time + C depending on the values of the studied implementation at the last time i - T. If there is no clock dependence

in general, i.e. (t -ft) / x (t), x (t-t (-t + t) / x (t) J, TO the process under study is Markovian.

5. Measurement of the function / U (T).

The nature of the dependence of the conditional distribution on x (t-T) values makes it possible to reasonably apply or reject the use of one-dimensional Markov mathematical models in the study of real random processes. The same kind of conclusions regarding the properties of the process under study, but more expediently allows you to do and function

() / x (tl, x (t-T) f (ttt) / x (tll which is introduced by analogy with the collision function

((t) et

Indeed, the fact of independence of the random variables x (t + t) and x (-t) can be learned from measuring only the density of distribution with x (-t -t / x (t)). If the type of this density does not depend on the value of b, then the random variables are independent. However, it is more expedient to draw such conclusions on the basis of a study of the properties of the collision function L (c), which is also true of the function U (T} with respect to determining whether the process under study is Markov.

The proposed device allows to measure the function ("(, T). To do this, it is necessary to close the contacts 10 and 11, 28 and 30, 31 and 32, 34 and 35, 48 and 50, 51 and 32, 54 and 55, 57 and 59, 61 n 62, 64 and 65 (see diagram).

Through contacts 48 and 50, the first 1 and second 17 inputs of the device are connected, and the implementation x (i) of the random process under investigation is simultaneously fed to the first inputs of the first key, second comparison circuit 40, first 2 and second 38 PIM. Pushing

eleven

buttons 67, the fourth trigger 44 is set to such a state that the second 41 and third 45 keys are open and the first 37 and fourth 46 are closed. From the auxiliary output of the voltage source 16, the threshold value X is set through the second open key 41 on the second comparison circuit. When the voltage of the implementation x / i at time t; exceeds the threshold x, at the output of the second comparison circuit, a pulse is generated which, after a delay at the time T in the second delay element 39, is output to the second input of the second modulator 38. At the same time, a count x (t; + t) is input at its output to the input the second amplitude selector 42, which is set to level x. and the width of the differential corridor is 4 x,. If the count x (tj + t) falls into the corridor Lh ,, then it is at the moment t; + T passes through the third element And 14 and enters the second inputs of the third 45 and fourth 46 keys. Through the open third key 45 and contacts 52 and 51 of the fourth additional switch, a pulse passes to the first input of the fourth element AND 20 is delayed by time t in block 22, and then breaks off the second trigger 18 and through the element OR 23 and the contacts of the fifth switch 25 and 24 enters to the second input of the first modulator 2. Thus, it is possible to collect statistics in the counter 5 to measure the probability distribution density CO Cx (t + f7x (t), X (i - T)).

In addition, the same pulse from the output of the second amplitude selector

42 at time t; + T through pins 64 and 65 of the sixth additional switch after a delay in the block

43switches fourth trigger

44 to another position, whereby the second 41 and third 45 keys are closed, and the first 37 and fourth 46 keys are opened. In this case, the second comparison circuit 40 does not work, and to the second input of the first comparison circuit 15 via the open first,

Key 37 receives the implementation of the process x (t) under investigation. From the voltage source 16, a threshold voltage x is established at the first input of the first comparison circuit 15. When the implementation x is exceeded (1 of this threshold

11912

In the code at time 1, a pulse is generated which, having passed through the third element H 14, the open fourth key 46 and the contacts 55 and 54 of the third additional switch, flips the second trigger 18 to its former state, passes through the fifth element I 21, the fourth element 47 delay, provide a delay of time -G, an element of OR 23 pins 25 and 24 of the fifth switch and at the time i c-T comes to the second input of the first modulator 2. This provides the possibility of typing statistics in the frequency divider 7 to measure the density W Tx (t + d / X Cirll.

The same pulse occurring at time i at the output of the first comparison circuit 15, after a delay in the block

43 rerun fourth trigger

44 in the initial state. In this case, the first 37 and fourth 46 keys are closed, and the second 41 and third 45 keys are opened. This creates an opportunity to take a count to estimate the density () / chad, v (t-T). The delay time in block 43 is chosen to be small, for example, equal to the pulse duration occurring on the codes of the second selector 42 of the first comparison circuit 15. The delay in block 43 requires that the third 45 and fourth 46 keys skip the corresponding impulses and only then be closed.

Thus, this determines the mode of operation of the first modulator 2, in which it is alternately constructed by pulses providing a set of statistics for measuring the probability densities of a species (JГx (x (t)

X (t –T j mso x (t + 1) / X (t I This 03 begins that the sample sizes of one and the other distributions collected during the analysis are the same. The estimate of the measured function is the ratio of the number C recorded in the counter 5, to the number D, recorded in the frequency divider 7,

The operation logic of all other units of the device remains the same as described when measuring the function of a collision.

The conversion factor of the divider frequency 7 must be chosen in the same way as when measuring the function of collie

1312

then, the estimate of the measured function is equal to fu C 10 and the device is directly indicative. This completes the measurement cycle of the function (C / T / for given x ,, x, T and J. To determine whether the process under study is Markov or not, when measuring the density y, t) / X It), Ut -T ) 1 and functions

/ T / f value can not be changed. It is only necessary to choose its value less than or equal to the correlation time of the process under study.

Claims (1)

Invention Formula A device for measuring the density of probabilities according to the auth. No. 390536, characterized in that, in order to expand the class of solvable 1x tasks, a second comparison circuit, a second, third and fourth delay elements, a fourth trigger, a second amperage-pulse modulator, a second amplitude selector, four keys, six additional switches and a second pushbutton switch, while the output of the second comparison circuit is connected via the second delay element to the first input of the second pulse-amplitude modulator, the output of which is connected via the second amplitude selector to the second the second input of the device through the movable and first fixed contacts of the first additional switch is connected to the information input of the first key, to the second input of the second pulse-amplitude modulator, to the first input of the second comparison circuit and through the disconnecting contact of the second additional switch the first input of the first amplitude-pulse modulator, the second fixed contact of the first additional switch is connected to the output of the first 0 one five s 0 5 o - 1914 key and the second input of the first comparison circuit, the second input of the second comparison circuit is connected to the output of the second key, the control input of which is connected to the auxiliary output of the voltage source, and the information input of the second key is combined with the information input of the third key and connected to the single output of the fourth trigger , the zero output of which is connected to the control inputs of the first and fourth keys, the first and second inputs of the fourth trigger are connected via the second push button switch, respectively, to the output the third delay element and to the first pushbutton switch; the fourth key output through the first fixed and movable contacts of the third additional switch is connected to the first input of the fifth element And; the second fixed contact of the third additional switch is connected to the output of the pulse generator; the fixed and movable contacts of the fourth auxiliary switch is connected to the first input of the fourth element And, the second fixed contact of the fourth additional A third switch is connected to the information inputs of the third and fourth keys, the third fixed contact of the fifth additional switch and the output of the third element I, the movable contact of the fifth additional switch connected to the input of the fourth element of the backup And the output of the fifth element I, the second fixed contact of the fifth an additional switch is connected to the output of the fourth delay element and to the first input of the OR element, the input of the third delay element through the opening contact of the second a further switch connected to the output of the first comparator circuit.