Method for generating test signal incorporating probability distribution function

FIELD: measurement technology; generating test signals with preset probability characteristics.

SUBSTANCE: proposed method for generating test signal incorporating desired distribution probability function F(x) concerning occurrence of instant test signal amplitude values x(t) depends on generation of original signal r(t) with uniform distribution of instant amplitude values within the range of 0 to 1 and its functional conversion; generated as original signal r(t) is determinated signal with period T0 for which purpose signal φ(t) varied obeying known law and using desired algorithm is functionally converted.

EFFECT: enhanced precision of generated signal incorporating desired probability distribution function.

1 cl

 

The invention relates to the field of measurement technology and can be used to generate test signals with precisely defined probabilistic characteristics, such as functions of the probability distribution (DAF)used in the simulation and verification of statistical measurement systems (SIS).

There is a method of generating a test signal with a given the probability distribution function F(x) of occurrence of the instantaneous values of the test signal x(t) [Levin BYR Theory of random processes and its applications. - M.: Owls. radio, 1957, C.], based on generating a set of source independent random signals with identical uniform distributions of the probabilities of occurrence of instantaneous values and their sum, and the number of components depends on the set of WDP.

There is also known a method of generating a test signal with a given WDP occurrence of instantaneous values of F(x) [work experience YG, V.A. Filimonov statistical machine modeling means. - M.: Radio and communication, 1988, p.63-65; Kleijnen j. Statistical methods in simulation. - M.: Statistics, 1978, issue 2, pp.272-275. 288), which generate a number of independent source of random signals with identical uniform distributions of the probability of occurrence of instantaneous values in the range from 0 to 1 and summer who have them with different weights, dependent on the set F(x).

The disadvantages of the above methods are:

- low accuracy of generating the test signal due to a systematic error of job uniform distribution and the statistical dependency of random signals:

- the presence of methodological random error arising due to the finite duration of exposure to random test signal in simulation and metrological certification SYSTEM;

- limited varieties of test signals.

Closest to the claimed method is a method of generating a test signal with a given distribution function of the probability of occurrence of instantaneous values of F(x) [Statistical models and methods in measuring tasks: Monograph / Sahabettin, Mevludin: Nizhny Novgorod. state technology. University, Nizhny Novgorod, 2000, pp.5-6, 33; Kleijnen j. Statistical methods in simulation. - M.: Statistics, 1978, issue 1, p.32-33], is based on generating the initial random signal r(t) with a uniform distribution of probabilities of occurrence of instantaneous values in the range from 0 to 1 and its functional transformations of the form F-1[r(t)], where F-1symbol function inverse to the function F(x).

The disadvantages of the prototype are:

- low accuracy of generating the test signal and the errors job uniform distribution of the initial random signal;

- the emergence of methodological bias arising from physical serializenode in General functional transformations of the form F-1[r(t)] for test signals with infinite positive and negative values, for example, Gaussian distribution, Cauchy. Rayleigh, etc.;

- the emergence of methodological random error arising due to the finite duration of exposure to random test signal in simulation and metrological certification SYSTEM.

The objective of the invention is to improve the accuracy of formation of the WDP test signal, an exception methodological random error arising due to the finite duration of exposure to random test signal in the simulation and verification SYSTEM, by generating deterministic test signals on the set of WDP.

The objective of the invention is achieved by the fact that, in the known method of generating a test signal, which generates the original signal r(t) with a uniform distribution of probabilities of occurrence of instantaneous values in the range from 0 to 1 and is subjected to its functional transformation of the form F-1[r(t)], where F-1symbol function inverse to the function F(x), according to the invention as the source signal to generate a deterministic process is the period of T 0why are extracted from the selected deterministic process parameter ϕ(t)varying but known to the law, and punish him for functional transformation algorithm

where Ψ(ϕ)) is the inverse function to the function ϕ(t)int(t/T0- the function "number" from the relationship t/T0, max(x(t)) and min(x(t)) respectively the maximum and minimum values of the deterministic test signal x(t).

Method of generating a test signal with a given WDP implemented as follows.

Suppose you want to generate a test signal of limited amplitude ±And with the Cauchy distribution F(x)=1/2+(arctan(x/α)/π, And<x<A. Use as the selected deterministic process, for example, changing the parameter for the exponential law ϕ(t)=U0exp(-t/RC), namely the change in the voltage between the plates of an electrical capacitor To discharge through its own resistance R of the dielectric of the capacitor when disconnecting the capacitor from a voltage source U0volt. From the analysis of algorithm (1) shows that the transformation needed to generate the original signal can be performed in several stages. First option ϕ(t) must be functional transformation ψ(ϕ(t)), reverse the function ϕ (t). Therefore, in the present case, the conversion ψ(ϕ(t)) must be implemented by algorithm RCln[ϕ(0)/ϕ(t)], where t=0 is the start of reading of the original exponential signal. When the technical implementation of the latter algorithm reads the value of the voltage between the plates of a capacitor at time t=0 and, then, the current time ticalculate and logarithmic their attitude. The following feet: calculate the difference F(max(x(t)))-F(min(x(t)))=F(A)-F(A)=2arctg(A/α)/π; in accordance with the algorithm (1) calculate and generate the current value of the original signal r(t) at time tialgorithm

Next, sequentially in time calculate and generate the current values of the original signal at specific points in time, thereby generating the desired source signal. To exclude the influence of the transient process when disconnecting the capacitor from the source exemplary voltage, it is necessary to skip a few periods of the test signal x(t) until the end of the transition process. For the selected variant of the original deterministic process technical implementation of the generator test signal x(t) possible different devices, the most successful of which is "computer generator" - a computer that calculates values and the output r(t) and the test signal x(t) and controlling the operation of digital to analogue Converter [Internet address http:phys.kemsu.ru/PhysDep /work %20 program / predmet/ HTMLS/ la2dac.htm), with the error of generating the test signal is not more than ±0.2%. In the apparatus of the prototype, only the source signal generator with a uniform distribution of occurrence of instantaneous values in the range from 0 to 1 makes the error of not less than 5% [Statistical models and methods in measuring tasks: Monograph / Sahabettin. Mevludin; Nizhny Novgorod. state technology. University, Nizhny Novgorod, 2000, p.7-8|, not counting the errors of the devices that implement the functional transformations of the form F-1[r(t)],

Using the proposed method can achieve much lower error formation WDP test signal, exceptions methodological random error arising due to the finite duration of exposure to random test signal in the simulation and verification SYSTEM than known methods.

Method of generating a test signal with a given the probability distribution function F(x) of occurrence of the instantaneous values of the test signal x(t), based on the generation of the original signal r(t) with a uniform distribution of occurrence of instantaneous values of the amplitudes in the range from 0 to 1 and its functional transformation of type F-1[r(t)], where F-1symbol function inverse to the function F(x), characterized in that the source signal r(t) generate deter nirovany signal with period T 0why carry out a functional transformation of the signal ϕ(t), evolving according to the known law, the algorithm

{Ψ(ϕ(t))/T0-int(t/T0)}{F(max(x(t)))-F(min(x(t)))}+F(min(x(t))),

where Ψ(ϕ(t)) is the inverse function to the function ϕ(t)int(t/T0is a function of the integer part of the number from the relationship t/T0, max(x(t)) and min(x(t)) respectively the maximum and minimum values of the deterministic test signal x(t).



 

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