RU2803254C1 - Probabilistic device for calculation of variance - Google Patents

Abstract

FIELD: automation and computer technology.

SUBSTANCE: invention is aimed at reducing the circuit complexity of the device for calculating the variance of a random signal and real-time processing of the input signal. It is achieved due to the fact that the device contains two D-triggers, four two-input AND gates, a reversible variance counter, a digital comparison circuit, a mathematical expectation counter, a clock pulse generator, a product counter, a counter for the number of statistical tests, a unit for transcription of results and a probabilistic converter.

EFFECT: reducing the circuit complexity of the device for calculating the variance of a random signal and real-time processing of the input signal.

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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 monitoring and control systems.

There are known devices for similar purposes, built on the basis of specialized arithmetic-logical devices, which consist of quadrators, dividers and adders [Porfiryev G.N., Barakhtin V.M. A device for calculating estimates of mathematical expectation and variance. AC SU 1280392 A1 publ. 12/30/1986]. Their main disadvantages are the relatively large hardware volume and low performance.

The problem to be solved by the claimed invention is the development of a device for calculating the dispersion of a random signal with a probabilistic representation of data, having a small hardware volume and the ability to process the signal in real time.

The solution to a technical problem is achieved by using a probabilistic form of data representation, and therefore the hardware implementation of basic mathematical operations changes.

The technical result provided by the above set of features is a reduction in the hardware volume of the device for calculating the dispersion of a random signal and the ability to process the input signal in real time, achieved by replacing digital comparators, dividers and adders in the prototype with accumulative binary counters.

For ergodic stationary random signals, time quantized in accordance with Kotelnikov’s theorem, the expression for estimating the dispersion has the form:

or

Where:

X(t) - measured random signal, represented in binary positional code;

N is the number of cycles of measuring the value of a random signal x _i .

K is the number of statistical tests required to convert the measured value of a random signal x _i into a probabilistic display, represented in a binary positional code.

In accordance with expression (2), to measure the dispersion of a random signal X(t), it is enough to carry out a linear probabilistic transformation of the measured random signal X(t), sum the terms of the probabilistic map over the measurement interval and assign the resulting value to the product N×K.

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

1 - probabilistic converter (which can be used - Moiseev D.V., Sapozhnikov N.E. Binary code converter - probabilistic mapping; Patent 2660831 Russian Federation, IPC N03M 7/00 (2006.01) publ. 07/10/2018 Bulletin . No. 18);

2.1 and 2.2 - D-triggers;

3.1 - 3.4 - two-input connectors;

4 - reverse dispersion counter;

5 - digital comparison circuit;

6 - mathematical expectation counter;

7 - clock generator;

8 - product counter N×K;

9 - counter of the number of statistical tests K;

10 - block of census results.

The processes in the circuit of the proposed device occur in the following sequence. At the start of operation, the values of counters (6) and (8) are reset, after which the calculation begins. The measured random signal X(t) is supplied to the inputs of the probabilistic converter (1) and the digital comparison circuit (5). From the output of the probabilistic converter (1), clocked by the clock pulse generator (7), the probabilistic display Y ₁ (t) is fed to the first input of the first two-input connector (3.1), the second input of which receives the same signal - the probabilistic display Y ₁ (t) with a delay of one clock cycle, from the output of the first D-flip-flop (2.1), the product Y _i (t) & Y ₁ (t-1) is formed at the output of the first two-input conjunctor (3.3), which is supplied to the first input of the third two-input conjunctor (3.3 ), the second input of which receives a signal from the N×K product counter (8), which is also clocked by the clock pulse generator (7), the output of the third two-input conjunctor (3.3) is connected to the summing input of the reversible dispersion counter (4), to the subtractive input of which a probabilistic display of the squared estimate of the mathematical expectation is _supplied from the output of the second two-input conjunctor (3.2), the first input of which is supplied mathematical expectation (m _x ) of the converted random signal X(t), obtained as a result of integration Y ₁ (t) in the counter m _x (6), into which it enters through the fourth two-input connector (3.4), the first input of which receives the value Y ₁ (t) from the output of the probabilistic converter (1), and the second input receives a signal from the product counter N×K (8), the second input of the two-input conjunctor (3.2) receives a signal from the digital comparison circuit (5) with a delay of one clock cycle from the output of the second D-flip-flop (2.2), at the output of the second two-input conjunctor (3.2), a probabilistic value is generated displaying the squared estimate of the mathematical expectation of the converted random signal X(t), which is supplied to the subtractive input of the reversible dispersion counter (4), in which it is formed variance value , which is transmitted to the results census block after N×K×K clock cycles, for which the circuit contains a counter for the number of statistical tests K (9).

The technical and economic efficiency of the proposed device for calculating the dispersion of a random signal based on the probabilistic representation of information consists in reducing its hardware volume while maintaining the accuracy characteristics and the ability to process the input signal in real time.

Claims (1)

A probabilistic device for calculating dispersion, characterized by the fact that the circuit includes two D-flip-flops, four two-input connectors, a reversible dispersion counter, a digital comparison circuit, a mathematical expectation counter, a clock pulse generator, a product counter N×K, a counter for the number of statistical tests K, a block census of results, a probabilistic converter, the input of which is the input of the entire circuit, to which a random signal X(t) is supplied, the probabilistic converter performs a linear probabilistic transformation of the measured random signal X(t), the second input of the probabilistic converter receives clock pulses from the clock pulse generator, output which is also loaded to the input of the product counter N×K, which counts clock pulses from the clock pulse generator, the output of which is loaded to the input of the counter for the number of statistical tests K, the output of which is loaded to the enabling input of the result census block, the output of which is the output of the entire circuit, to the information input which the output of the reverse dispersion counter is loaded, the summing input of which is loaded with the output of the third conjunctor, the first input of which is loaded with the output of the first conjunctor, the first input of which is connected to the output of the probabilistic converter, the second input of which is loaded with the output of the first D-trigger, the information input of which is also loaded the output of the probabilistic converter is connected, the output of the N×K product counter is loaded to the second input of the third conjunctor, the output of the second two-input conjunctor is loaded to the subtracting input of the reversible dispersion counter, the first input of which is connected to the output of the digital comparison circuit, the output of the second D-flip-flop is loaded to the second input, the information input of which is also connected to the output of the digital comparison circuit, the input of which is loaded with the output of the mathematical expectation counter, the input of which is connected with the output of the fourth two-input conjunctor, the first input of which is connected with the output of the probabilistic converter, the second input is loaded with the output of the N×K product counter, synchronization the entire circuit is carried out from the output of the clock generator.

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