RU2771593C1 - Probabilistic apparatus for calculating the average total power - Google Patents

Abstract

FIELD: computing technology.

SUBSTANCE: invention relates to the field of automation and computing technology and can be used for measuring the characteristics of random processes in automatic control and regulation systems.

EFFECT: development of an apparatus for calculating the average total power of a random signal with probabilistic display of data, providing a possibility of reducing the hardware size of the apparatus compared to similar digital apparatus, due to the use of a probabilistic form of representation and conversion of signals and the arithmetic operation of multiplication being performed on probabilistically represented data.

1 cl, 1 dwg

Description

The invention relates to the field of automation and computer technology and can be used to measure the characteristics of random processes in automatic control and management systems.

Known devices for a similar purpose, built on the basis of specialized arithmetic logic devices [Vasilenko A.D., Kutasevich V.P., Musich Yu.V. A device for measuring the average power of signals in channels and paths of communication systems. AC SU 10950831 publ. May 30, 1984]. Their main disadvantages are relatively large hardware volume and low performance.

The task to be solved by the claimed invention is the development of a device for calculating the average total power of a random signal with a probabilistic representation of data with a small hardware volume and the ability to process a signal in real time.

The solution of the technical problem is achieved by using a probabilistic form of data representation, in connection with which the hardware implementation of the main mathematical operations changes.

In general, the essence of the stochastic or probabilistic transformation of information into a non-positional probabilistic mapping is that any value of the converted value can be associated with a certain probability - the probability that the value of the converted value will be greater than the value generated randomly within the range of the converted value.

In the simplest case, the value of the parameter of the converted quantity is either always positive or always negative, and the conversion process itself is performed in accordance with the rule:

where x _i - ie the value of the parameter of the converted signal X(t);

R(t _ij ) - je the value of the auxiliary random signal parameter R(t), changing in the range of X(t);

- число циклов преобразования сигнала X(t);

- number of signal conversion cycles X(t);

- количество статистических испытаний каждого значения x_i, внутри временного интервала Δt_i=t_i+1-t_i;

- the number of statistical tests of each value x _i within the time interval Δt _i =t _i+1 -t _i ;

y _ij - the value of the probabilistic display of the signal parameter x _i , from the series

A probabilistic mapping has the properties of synchronism (clocking) and independence of each member of the mapping from any other.

The first property is that the formation of members of the probabilistic mapping is carried out at a constant time interval Δt _i =t _i+1 -t _i , determined by the frequency ƒj=1Δt _j of the rule (1).

The property of independence of each member of the probabilistic mapping y _ij from any other follows from the fact that obtaining a probabilistic mapping corresponds to the Bernoulli test scheme. For a random sequence obtained in accordance with this scheme, the autocorrelation function is a δ-function at τ=0. To prove this, it should be shown that the repeated tests in accordance with (1) are also independent. The values of the auxiliary random function R(t) are formed at discrete times. At any time, a function can only be in one of its states r _tj with probability P _j (t). Obviously, for any t

and for given probabilities P _j (t) the distribution r _ij can be given by the probability density:

where

is the distribution of a fixed quantity r _ij determined by the Dirac function.

The use of these properties and the use of probabilistically presented discrete signals makes it possible to simplify functional units for performing arithmetic and logical operations, in particular, addition, subtraction, multiplication, raising to an integer power, division, comparison, etc. and, thereby, sharply reduce their hardware volume.

Given the original transformation rule, the probabilities of the occurrence of "1" and "0" in the probabilistic display are:

The mathematical expectation of a probabilistic mapping is determined through a distribution series for a discrete random variable y _and

Then

Thus, the probability of the appearance of "1" in the probabilistic display is the mathematical expectation of the display and is numerically equal to the value of the integral distribution law of the auxiliary signal R(t) at the comparison level x.

Of particular interest is the case when the auxiliary random signal R(t) obeys a uniform distribution law in accordance with

For it, the last expression for the mathematical expectation (2) will be rewritten as:

those. we have the case of a linear probabilistic transformation.

The implementation of computing devices that perform arithmetic and logical operations on probabilistic mappings leads to a multiple reduction in the hardware volume of the computing device, and the probabilistic representation and transformation of information itself provides noise immunity and cryptographic stability of the processed and transmitted information.

The technical result provided by the above set of features is to reduce the hardware volume of the device for calculating the average total power of a random signal and the possibility of processing the input signal in real time, achieved by performing an arithmetic multiplication operation on probabilistically presented data.

For ergodic stationary random signals, quantized in time in accordance with the Kotelnikov theorem, the expression for estimating the mathematical expectation (3) has the form:

where N is the sample size of the measured random process X(t).

будет:Considering that in a one-line unipolar probabilistic transformation, each value is replaced by the corresponding probabilistic mapping, the estimate x _i i.e.

will:

Substituting the last expression into the expression for calculating the estimate of the mathematical expectation and, to simplify the notation, replacing {M[X(t)]}* with m _x *, we obtain an expression for calculating the estimate of the mathematical expectation in the probabilistic form of information representation

or

The measurement of the average total power of a random signal differs from the measurement of the average in that it is not x(t) that is averaged, but its square.

Then, for ergodic stationary random signals, quantized in time in accordance with the Kotelnikov theorem, the expression for estimating the average total power has the form:

In accordance with this expression, the device for calculating the estimate of the average total power of a random signal should consist of two probabilistic converters, a clock generator, two conjunctors for two inputs and two accumulative counters - a result counter and a product counter N*K.

The essence of the invention is illustrated by the drawing Fig., which shows a functional diagram of a probabilistic device for calculating the mathematical expectation, where:

1.1 and 1.2 - probabilistic converter (which can be used - Moiseev D.V., Sapozhnikov N.E. Binary code converter - probabilistic display; Pat. 2660831 Russian Federation, IPC H03M 7/00 (2006.01) publ. 10.07. 2018 Bull. No. 18);

2.1 and 2.2 - two-input connector;

3 - result counter;

4 - clock pulse generator;

5 - counter product N×K;

6 - block of census results.

The input measured random signal is simultaneously fed to both probabilistic converters (1.1 and 1.2), where the signal is simultaneously quantized in time, due to clock pulses from the clock generator (4), in accordance with the Kotelnikov theorem, and the probabilistic transformation of each quantized value x _i , into probability mappings Y _1i (t) and Y _2i (t). Their multiplication is carried out on the conjunctor (2.1). When the counter of the product N × K (5) overflows, its output signal blocks the arrival of the probabilistic square mapping (average total power) through the second conjunctor (2.2) to the result counter (3) and gives the value of the estimate of the average total power through the census block (6) to schema output. The digit capacity of the counters is selected based on the required accuracy of measurements and calculations, as well as the bandwidth of the meter.

The technical and economic efficiency of the proposed device for calculating the average total power of a random signal based on the probabilistic representation of information consists in reducing its hardware volume while maintaining accuracy characteristics and the possibility of processing the input signal in real time.

Claims (1)

A probabilistic device for calculating the average total power, characterized in that the circuit includes a clock generator, a product N * K counter, a result counter, a result census block, two conjunctors for two inputs and two probabilistic converters, the inputs of which are the input of the entire circuit, on which a random signal X(t) is supplied, the probabilistic converters simultaneously perform a linear probabilistic transformation of the measured random signal X(t) into a probabilistic display, the second inputs of the probabilistic converters receive clock pulses from the clock pulse generator, the output of which is also loaded to the input of the product counter N * K , which counts clock pulses from the clock generator, the output of which is supplied in direct code to the second input of the second two-input conjunctor, the first input of which is loaded with the output of the first two-input conjunctor, the inputs of which receive probabilistic mappings Y ₁ (t) and Y ₂ (t) from to outputs of probabilistic converters, the output of the second two-input conjunctor is loaded on the input of the result counter, the outputs of which are loaded on the inputs of the result census block, on the resolving inverse input of which the output of the N * K product counter is loaded, the output of the census block is the output of the entire circuit.

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