DE2241312C3 - Stochastic electronic generator - Google Patents

Description

2. Device according to claim 1, characterized in that. · · U <-ι · 1. -I indicates that the reading of a counter (16), which is now switched on with statistical equalization, results in random numbers in the interval 0 < w <1. It is correct which of several possible and subordinate them to the mean values given by equation (3) is set, so that a »5 transformation is obtained, according to M g. 1 lur t ₀ sequence of random distances with different exponentially distributed values

Mean values is generated (Fig. 6). The disadvantage of this method is that d.e

3. Device according to claim 1 and 2, characterized in particular by transformation according to equation (3) characterized, that by the reading of the counter the infinity place of the natural logarithm, (16) at the clock generator (14) a certain clock 30 can be carried out only with difficulty and some frequency and the random generator (15) requires a loading effort. In addition, the first must then Probability is set (Fig. 6). held values are implemented in time intervals

4. Device according to claim 1 and 2, thereby.

characterized that by the reading of the counter. Threader is another well-known method at

at the clock generator a certain clock frequency 35 which the continuous exponential distribution through

is set. a discrete distribution is approximated. For this

5. Device according to claim 1 and 2, thereby the geometric distribution that one is suitable characterized in that the reading of the counter according to F i g. 2 think emerged in the following way a certain truth can on the random event generator.

probability is set. 40 At equidistant points in time, 17

6. Device according to claim 1, characterized in that a random event with the constant probability that the frequency of the clock probability P occur. The resulting errators (18) of a random frequency modulation event have time intervals that are all completely subject to (FIG. 7). are numerous multiples of AT . The probable

7. Device according to claim 1, characterized in that a distance is exactly / ;. 17 * indicates that either the clock at a pit - η AT) = (1 - ργ-ιρ for η > 1 (4) any point in the circuit or the output pulse of the random event generator over there the random event exactly ( n - l) times a delay element (19) is not passed, which may occur and which finally occurs once Delay time is changed randomly (FIG. 8) 50 The electronic generation of random events

certain probability is due to so-called

Random Event Generalists in a number of known ways

possible. There are both real random

The present invention relates to the electronic events (K ο r η e r, A., Linsbauer. W.

Generation of random events in statistically ex- 55 Schäff er, B. and Wehrmann, W .. Elcktro

onentially distributed time intervals. Nischc creation / cugation of stochastic slave processes. di;

For a better understanding of the following, it should be determined by stationary Markol chains

term of the exponential distribution are briefly explained Arch, elektr. Ubcrtr. 21 [1967], p. 23) as well as pseudo ·

cn. A time interval t is then exponentially random system (Hartley, M. Cl .: Development

granted if for the probability that 1 greater than 60 Design and Test Procedures for Random Generatoii

If any given value / "is, the following applies: Using Chaincodes, Proceedings IFiE, vol. 11 (\ .lan

, ^ _ (_, it \ m 1969, pp 22 to 34) into consideration.

itV ..- r _o > - expi -I ₀ Hm) (W ^ ₀ j.- _ormc | ₍ , ^ gives a geometric statistical

Here, m is the mean value of the distribution to which the distribution of the line spacings is again

) ichtefunction ⁶ 5 values, plotted as a function of η, brilliant

.. _n , _. . _{IT Λ m} F i g. 3 lie on an exponential curve. DadurcF

p (t) - U // m) expt - /, / m) U) _{jst die Mrti!} ij _c | _lkc ; _t given, the Γ-xponentialvcrtei

heard. approach. This method was used for the Bai

used on a transport machine (Broadhurst S. W .. Harmston, A. T .: An electronic traffic analyzer; The Post Office Electrical Engineers Journal, January 1950, vol. 42, part. 4, p. 181).

In the arrangement according to Broadhrrst ' Harmston is not a systematic possibility, however given to change the mean value of the pulse intervals. For a wide range of applications of such a Poisson pulse generator it is

Applications not the time average, but rather the average pulse frequency. For these applications do not have to be the mean value

The clock source 1 of a fixed frequency has a clock spacing J T ₀ . Any number of decimal frequency dividers 2, 3, 4 etc. connected in a chain produces clock pulses at points a, b, c etc. at a distance of J T ₁₁ , 10 J T ₀ , 100 J T ₀ etc. One of these points is selected via the rotary switch 5 and fed to a preset counter 6, 7, which works as a variable frequency divider. The preselection

-.-j- counter counts the pulses at its input,

but it is necessary to adjust the mean value to any io until it has reached the preselected level. In this To be able to adjust the value. In addition, if there are many moments, a pulse is emitted at output 11

and the counter is reset. There are many known possibilities for the construction of such counters. In the exemplary embodiment according to FIG. 5 will

Instead, the reciprocal mean pulse frequency 15 used by a hundred counter 6, which has the positions 0 can be set precisely. can go through to 99 and its position through

The present invention now enables evaluation by a downstream coding circuit 7 a simple, predominantly digital circuit is approximated, that on the number of tens corresponding to the position to generate Poisson-distributed pulses, and a logical one occurs on the ones output optionally both the mean pulse spacing 20 but all other outputs being a logic zero. as well as its reciprocal value, the mean pulse rate. Rotary switches 8 and 9 set a counter frequency, can be set precisely. position selected. If the counter reaches this

The invention relates to a device, the selected position, so arises via the AND gate 10 from a clock generator with fixed or adjusting a pulse at its output, which also the barem clock interval and also from a random 25 counter in the position Resets zero. Is an example event generator that, when triggered with a clock rate as in FIG. 5 the counter reading 62 is set, so a pulse with a fixed or adjustable probability - this has the consequence that after 62 clock pulses Veit always delivers output pulses with a certain average at the input of the counter 6 a pulse at the output 11 value of the time intervals, and is created. With this, however, the A Γ value can essentially be characterized in that a fixed clock interval is set at the 30 gear with any integer, digital one-clock generator, or a w-fold multiple of a basic interval is set for the adjustable value between one and one hundred multi-clock interval and that the random event generator has a fixed probability
or a /? - multiple of a basic probability 35
is adjustable so that when the random event generator is triggered by the clock generator,
the mean values of the output impulses a / »// i times
Form a multiple of a basic mean.

The idea of the invention is to be explained in more detail on the basis of the characters. Fixed clock rate, for example 10 kHz, results in FIG. 1, 2, resulting in an AT ₀ of 100 μ &. The constant 3 and 4 will represent known methods. The F i g. 5 probability Pah assumed to be a hundredth, and 6 show examples of the structure of the invention, so that a circuit according to equation (5) is obtained, and the F i g. 7 and 8 explain 100 (is / 0.01 = 10 ms. If the switch 5 on the ei-ic is an additional measure, which is a property of 45 points, then the preset counter Λ T ₀ and the generated distribution can be improved the mean with a factor between

One and one hundred can be multiplied so that the mean value can be set between 10 ms and 1 s in steps of 10 ms. With the help of switch 5, AT at the input of counter 6 can also be multiplied by 10, 100, 1000 etc. by the constant frequency divider, which corresponds to a multiplication of the set mean distance by 10, 100, 1000 etc. With the switches 8 and 9 the numerical value can be adjusted, with the switch 5 the order of magnitude of the desired mean value can be adjusted.

If the preselection counter 6, 7 is made up of η decadic consecutive counting stages, then

is the value of / '. This determines the ratio 60 of the numerical value for T _m to η decimal places exactly between 7 ',,, and the time interval I T. One can be set.

According to the possibility it is. for P a fixed to this in FIG. 5 shown embodiment

Wcrl set that is small enough to hear the expo some variants. Thus, either the chain can be approximated to the desired application of the fixed frequency divider or the variable frequency divider, and the mean frequency divider can be omitted if only mean values in a value are determined by varying the duration AT Scope are to be generated. The counting diM-n. scope of the counter working as a variable divider

FIG. 1 shows an example of an embodiment for this. 5. Can be anything. The fixed fre-

be plicated. With the thus obtained clock pulses adjustable interval, a random event generator 13 is triggered again, at the output 12 of which a pulse occurs with the probability I 'with each trigger. These impulses then have the desired spacing distribution.

A numerical example should make the function of the circuit even clearer: Is the frequency of the primary

The only one to be selected in the case of the exponential distribution The parameter is the mean. The mean of the geometric described by equation (4) Distribution is calculated to

ir

It can therefore be influenced both via 1 T and via the probability / '. From Fig. It can be seen from an example that the smaller the axial distribution, the better it is approximated

sequence dividers have arbitrary partial ratios, their number is unlimited.

In the previous explanations, a random event generator 13 with a fixed probability / 'was assumed, with the variation of 7', "by .17". According to equation (5), however, T _m can only be changed by the value of / ' .

For certain applications, it is not primarily the mean distance 7 " _{m between} the random events that is important, but the mean frequency of the random events /", 1/7 ". For them, according to equation (5)

AT

(6)

f _m is therefore directly proportional to the because of / 'and can be set in decadic steps by means of a decadic graduation of /'. So you get z. B. for

>' ² ' ³ /

_Moo , _M00 , / _{1 (l0} ,

·' ' for

_{/ 100} , 1 ₁₀ IUi

i / 1 7-2 / Ir 3/17 · g 17 "1 / 17'IT

/ 100 · '' ι / 100 · '' ■ -loo -Ii, ..., / Km · I ', / 10 ■ 1 1 ■ ■ I i can again be determined by a chain of decadic frequency dividers by any power of ten can be increased so that the desired value for / ", again according to the numerical value and the order of magnitude, can be set.

If a random event generator is used in which a value _{nP B} can be selected for the probability P , which is an integer multiple of a basic value P _n and, on the other hand, a variable frequency divider is used with which the AT multiplies by an integer value m at the input of this divider can be, it follows

T _m -

m AT η P _n

and f _m -

η ί Po m \ AT

In this way, however, any rational numerical ratio can be set for T _m or for f _m. The m is set digitally on the variable frequency divider, the η on the random event generator. By switching on a certain number of fixed frequency dividers, the value for T _m and f _m given by m and η can be increased or decreased by certain factors (for example by powers of ten).

The generation of a specific mean value T _m according to the invention also makes it possible in a simple manner to have random intervals with different mean values follow one another. A corresponding circuit, given by way of example, is shown in FIG. 6. It consists of a clock generator 14 which controls a random event generator 15. In addition, the circuit also contains a counter 16, the status of which is intended to indicate which mean value is currently to be generated. If random intervals with the η mean values T _mi , T _m2 , T _m3 , ..., Tmn are to be generated in a cyclical sequence, each Ti can be replaced by a certain Δ Ti (from the clock generator) and a certain 1 \ (by the random event generator).

The function of this circuit is as follows: The clock generator 14 is designed in such a way that it, switchable by logic signals, can generate the η clock frequencies with "17" up to AT _n . On the other hand, the random event generator 15, likewise switchable by logic signals, supplies the η probabilities P, to P _n. the counter 16 indicates which average is about to be generated. It is g in F i. 6, for example designed as a ring counter, so as a feedback shift register with η points, in which a single logic 1 cycle If the counter is in position 1, the value.! Ti is selected by the logical 1 at the / th position of the ring counter on the clock generator and the value Pt on the random event generator. If with this setting a random event occurs at the output of the random event generator , which corresponds to the realization of a random distance with the mean value 7 " _m t, the counter is simultaneously advanced by one place, i.e. However, Amit set ATIN ^nd Pi-n, and thereby generates a random distance next to the mean 7 _"m <j +, etc. in a cyclical succession.

The generation of the various ATi can again be carried out as in FIG. 5 are carried out by fixed and variable frequency dividers, so that the selection of an AT ₍ corresponds to the selection of a certain partial ratio. It is also possible to use a random event generator with constant probability, and to switch only the clock frequency through the counter 16 or a constant clock frequency and a Switching the probability to be provided.

The generation of random events described here with approximately exponentially distributed distances it brings with it that the random events can only occur in a fixed cycle pattern for a set mean value. This can be for certain Applications have disadvantages. For example, if the circuit is used in conjunction with a If a system is used that has exactly the same clock frequency, the resulting random events would have always the same phase position for this cycle. This disadvantage can be avoided by using the basic clock is subjected to a random frequency modulation. The frequency deviation is so small chosen that the shape of the distribution and the mean frequency are practically not changed. F i g. 7th shows an example of an implementation. A clock generator 18 is used, the frequency of which is through a connected noise voltage 17 is controlled at random.

Another possibility exists according to FIG. 8 in it, the basic bar, the bar at any other point of the circuit or to conduct the random pulses themselves via a delay element 19, whose Delay duration is randomly changed again by a noise voltage 17, for example. Even this ensures that the random events generated no longer fall within a fixed clock pattern.

For this purpose 3 sheets of drawings

Claims (1)

ι 2 To generate this distribution, a natural process can be used as is known, the patent claims. befits even such a distribution. A -τ- ι. na: cn, vi Hsfiir is the radioactive decay of atoms. 1. Device, consisting of a Tag- ^^^ Geiger-Müller counter tube registers generator with test or adjustable clock- 5 of the ^{preconditions determined with e} ^ ^{em fc} and a random generator, which can be unier υ Imnulse exno trigger with a clock pulse with fixed or have d, _e from ZaMnJj ^^ J ^^ Z ] adjustable probability output pulses "^ '^ ^^ _r ^ ™ _te finds this method with a certain mean value of the temporal speed of radioactive rrapa Gives off distances, thereby geken nzeich- χ- ^^ i method assumes. net that at the clock generator a fixed clock- A and eres oe kdiu ^u "" lpirhvprteiher \ Wl distance or for the pitch one, »- times that by a 'Jransfonnation' ^ ^h ^ ^rte ^ ^{r M} ^" Multiples of a basic distance can be set, any values can be generated. can and that at the random event generator. The transformation ^ to about The fixed probability or a factor of 15 is the inverse of the distribution function Set multiple of a basic probability - here considered ^ f ^^ Z ^ LtZ p! is bar so that the mean values of the output inverse function to calculate equation (1), hs impulse an »i / n -fold multiple of a basic result average if the random event _ _T j _n , (M ^) generator is triggered by the clock generator. 2 ° ° ™ \ w J