RU1777160C - Device for determining static characteristics of random processes - Google Patents

Abstract

The invention relates to measuring technique and can be used to measure dispersion, third and fourth cumulants and determine the asymmetry and excess coefficients. The purpose of the invention is to expand the functionality by measuring the third and fourth cumulants and determining the asymmetry coefficient. The dispersion of the process is measured using the zero modulation method according to the reference Gaussian noise with the following set of elements with the corresponding connections: switch 1, amplifier 2 with variable gain, adder 7, quadrator 8, multiplication unit 10, centering filter 13, amplifier voltage 16, noise generator 4, amplifier 3 with adjustable gain, clock generator 5. Measurement of cumulants is based on a comparison of the total powers of quadratically converted the reference noise and the analyzed process with the equality of their variances at the output of the second quadrator 9. The signals are extracted by synchronously detecting the signal, quadrator 9 using the multiplication unit 12, the centering filter 15, the multiplication unit 11, the centering filter 14. The zero offset of the quadrator 8 by setting the reference voltage The voltage U allows obtaining a signal of a quadrator 9 with a component proportional to the third cumulant. Periodic inversion of the signal in an amplifier with a changing sign of gain 2 with a frequency twice as low as the modulation frequency allows separation of signals proportional to the third and fourth cumulants when synchronously detecting the signal from the output of quadrator 9. The registrar 17 converts into a digital code signals proportional to the dispersion of the third and fourth cumulants, determines the asymmetry and excess coefficients, and displays the results obtained. The reference oscillations for synchronous detection are generated by a clock generator 5 and a clock divider 6. 1 il. (L C VJ XI VI o

Description

The invention relates to measuring technique and can be used in the study and classification of random processes for measuring variance, the third and fourth cumulants of the probability distribution of a random process, including against a background of Gaussian interference, as well as determining the asymmetry and kurtosis coefficients.

A device for determining the statistical characteristics of random processes, containing a quadrator, output

which is connected to the input of the first centering filter and the first input of the multiplication unit, the output of which is connected to the input of the second centering filter, an adder, an inverter, a voltage amplifier and a linear amplifier with an adjustable gain, the control and information inputs of which are connected respectively to the outputs of the voltage amplifier and the first centering filter, and the output through the inverter is connected to the first input of the adder, the output of which is connected to the second input of the multiplication unit, the output of the second centering The filter is connected to the input of the voltage amplifier, and the second input of the adder is connected to the output of a quad, the input of which is the input of the device.

The device measures the variance of a random process by quadration, followed by averaging. By adjusting the signal level proportional to the dispersion of the process, it is ensured that it is equal to the power value of the variable component of the process after the quadrator. The value of the conversion coefficient of the signal proportional to the dispersion determines the estimate of the excess coefficient, shifted by a constant value.

The disadvantage of this device is the inability to measure such statistical characteristics as the third and fourth cumulants, which determine, in particular, the asymmetry coefficient. This does not allow the use of the device for reliable classification of random processes, as well as processes entering the input of the device in an additive mixture with a Gaussian noise. In addition, the device determines the kurtosis coefficient shifted by a constant value, which also complicates the operational classification of processes.

The closest in technical essence to the present invention is a device for determining the statistical characteristics of random processes, containing a quadrator, the input of which is the input of the device, and the output of the quadrator is connected directly to the first input of the multiplication unit, and to the information input through the first centering filter an amplifier with an adjustable gain, the control input of which is connected to the output of a voltage amplifier, the input of which is connected to the output of the second centering fil fast, clock, amplifierjc

with a changing sign of the gain and the switch, the first information input of which is connected to the output of the quadrator, and the second information input of the switch is connected to the output of the amplifier with a variable gain, the output of the switch is connected to the second input of the multiplication unit, the output of which is connected to the information input of the amplifier with sign of the gain, the output of which is connected to the input of the second centering filter, and the control inputs of the switch and amplifier with a variable sign of the coefficient gain factors are connected to the output of the clock generator,

This device measures the variance of a random process by squaring and then averaging. The signal obtained by raising the analyzed process to the fourth power is compared in adjacent time intervals of the operation of the device with the signal obtained by multiplying the square of the analyzed process by a component proportional to the variance of the process. By adjusting the component proportional to the dispersion, equal signals are ensured. Using the magnitude of the conversion coefficient of the component proportional to the variance, a statistical characteristic is determined that is proportional to the offset value of the excess coefficient.

A disadvantage of the device is the impossibility of measuring the cumulants of the third and fourth orders and determining the asymmetry coefficient, which does not allow one to reliably classify the analyzed processes, especially when they are noisy by Gaussian noise.

The aim of the invention is to expand the functionality by additionally measuring the third, fourth cumulants and determining the asymmetry coefficient of the probability distribution of the random process.

This goal is achieved in that in a device for determining the statistical characteristics of random processes, comprising a first quadrator, a first and second centering filters, an amplifier with a variable gain, a variable-gain amplifier, a voltage amplifier, a first multiplication unit, a switch and a generator clock pulses, the output of the first quad being connected to the input

the first factor of the first multiplication unit, the output of the first centering filter is connected to the input of the voltage amplifier, the output of which is connected to the input of the gain value of the amplifier with an adjustable gain, the output of which is connected to the first information input of the switch, the control input of which is connected to the output of the clock generator pulses, a noise generator, adder, second and third multiplication units, a second quadrator, a third centering filter, a recorder and a frequency divider, etc. whereby the output of the noise generator is connected to the information input of an amplifier with a controlled gain, the output of a voltage amplifier is connected to the registration input of the variance of the recorder, the input of the first multiplication unit is connected to the input of the first centering filter, the input of the second factor of the first multiplication unit is combined with the input of the first factor of the second multiplication unit , with the input of the frequency divider and connected to the output of the clock generator, the output of the first quadrator is connected to the input of the second quadrator, the output to which is connected to the input of the second factor of the second multiplication unit and the input of the first factor of the third multiplication unit, the input of the second factor of which is combined with the input of the sign of the amplifier with the changing sign of the gain and connected to the output of the frequency divider, the outputs of the second and third multiplication units through respectively the second and the third centering filters are connected to the inputs of the registration of the fourth and third cumulators of the recorder, respectively, the input of the first quad is connected to the output of the adder a, the first input of which is the input of the reference voltage setting of the device, and the second input is connected to the output of the amplifier with a variable sign of the gain, the information input of which is connected to the output of the switch, the second information input of which is the information input of the device.

The introduction of new elements and corresponding relationships allows us to expand the functionality of the proposed device by measuring, along with such statistical characteristics as the dispersion and kurtosis coefficient, the third and fourth cumulants of the probability distribution of the analyzed process and, based on them, determining the asymmetry coefficient B differences from

moments, the third and fourth cumulants are dispersion independent characteristics. Owing to such invariance, the dispersion stabilization scheme in the device is simplified and the error in measuring the dispersion has little effect on the estimates of the third and fourth cumulants. Measuring cumulants in the proposed device expands its capabilities, allowing for these

statistical characteristics to detect, isolate and classify the process against the background of additive Gaussian interference. It will be possible to detect such changes in the process when its power remains constant.

The measurement of the third and fourth cumulants in the proposed device is based on a comparison of the total powers of the quadratically transformed reference

Gaussian noise and the random process being analyzed, applied to the input of the device at adjacent identical time intervals with equal values of their dispersions,

Ensuring the equality of dispersions and measuring the variance of the analyzed process is carried out using a zero modulation measurement method. The modulation frequency is selected as standard for modulation reception. Using well-known relations (see A.N. Malakhov, Cumulative analysis of random non-Gaussian processes and their transformations. M., Soviet Radio, 1978.

p. 250 ... 252), with an arbitrary form of the distribution density of the device’s own noise, the full signal powers after a quadratic transformation with a known constant offset of 1 G can be

represent by expressions: for a reference centered stationary Gaussian noise

45

 L2

P - + 4uW3y + 4u4Dy + Dr) +

+ 2 (Dy + Dr) 2 + (Dy + Dr) + (1a)

fifty

for the analyzed centered stationary process:

P A2 {W4X + W4y + 4u (W3 + L / s) +

4i / (Dx + Dy) + 2 (DX + Dy) z +

2i2

+ Px + Dy) + UT),

(sixteen)

where A is the transfer coefficient of the first quadrator;

A / zu. L / 4U - the third and fourth cumulative noise of own noise:

L / s. L / 4X - the third and fourth cumulants of the analyzed process:

Dy, Dx, Dr-dispersion of the intrinsic noise of the device, the analyzed process and the reference Gaussian noise.

With the equality of the variances of the reference Gaussian noise and the analyzed process

Dr dx

(2)

the difference in total powers after the first quadratic transformation is determined by the expression

dP A2 (W4x + 4uW3x)

(3)

Thus, the characteristics of the intrinsic noise of an arbitrary kind are not included in the expressions for the difference in total powers. A signal proportional to the difference in total powers is allocated in the device as a constant component after the second quadratic transformation. To separate the components proportional to the fourth W4X and the third L / C cumulants, at a given bias and the first quadratic transformation, a periodic inversion of the input process under analysis is used, with a frequency twice as low as the modulation frequency. In this case, the third cumulative factor Wax changes sign, which makes it possible to compensate for the term 4A when measuring the fourth cumulant L / 4X (see expression (3)) and select the component 4A uWax proportional to the third cumulant L / sx in a separate channel with a synchronous detector . With a known bias, this also makes it possible to determine the third cumulant L / sx.

The drawing shows a structural diagram of the proposed device.

The device comprises a switch 1, an amplifier 2 with a varying gain sign, an amplifier 3 with an adjustable gain, a noise generator 4, a clock generator 5, a clock divider 6, an adder 7, the first 8 and second 9 squares, the first 10, the second 11 and third 12 multiplication units, first 13, second 14 and third 15 centering filters, voltage amplifier 16, recorder 17.

The device comprises a switch 1, made, for example, on the basis of analog switches in the integral design of the 590 series, or using balancing transformers on long lines and identical switching diodes. The second information input of the switch 1 is the input of the device, and the first information input is connected

to the output of an amplifier with an adjustable gain 3. The control input of the switch 1 is connected to the output of the clock generator 5. The output of the switch 1 is connected to the information input of the amplifier with a variable sign of the gain 2, the sign reference input of which is connected to the output of the clock divider 6. An amplifier with a variable sign of gain 2 can be made, for example, in the form of a series connection of a balancing transformer on long lines, a switch (similar renno5 mu above) and a low noise amplifier with a constant gain factor and the desired frequency band. The output of the amplifier with a variable sign of the gain 2 through the second input of the adder 7, made in the form of a reference voltage controlled by the first input and a constant level component of the signal shifting circuit, is connected to the input of the first quadrator 8. The output of the quadrator 8 is connected

5 with the input of the second quadrator 9 and with the input of the first factor of the first block of multiplication 10, the input of the second factor of which is combined with the input of the first factor of the second block of multiplication 11,

0 with the input of the frequency divider 6 and is connected to the output of the clock 5. The output of the first block of multiplication 10 is connected to the input of the first centering filter 13, the output of which is connected to the input

5, a voltage amplifier 16, the output of which is connected to the input of the gain value of the amplifier with an adjustable gain 3 and the dispersion registration input of the recorder 17,

0 The output of the second quadrator 9 is connected to the input of the second factor of the second block of multiplication 11 and to the input of the first factor of the third block of multiplication 12, the input of the second factor of which is connected to

5 by the output of the clock divider 6. The outputs of the second and third blocks of multiplication 11, 12, through the second and third centering filters 14, 15, respectively, are connected to the inputs of the registration, respectively

0 of the fourth and third cumulators of the recorder 17. Squared 8 and 9, identical in circuit design, can be performed, for example, on the basis of broadband analog multipliers in the integrated design, or using balanced modulators on diodes with a quadratic characteristic, for example, inverted , and balancing transformers on long lines x. All multiplication blocks, like all centering filters

identical to each other. Multiplication units can be made on the basis of integrated multipliers or balanced modulators, and centering filters can be performed as low-pass filters based on active RC structures. The voltage amplifier 16 can be implemented on standard integrated operational amplifiers. Clock 5 is a standard square wave oscillator based on integrated digital circuits and generates a frequency and level stable waveform with a duty cycle of two. The clock divider 6 is also made on digital circuits and divides the main clock frequency into two oases. Either a standard noise source or a generator based on digital pseudorandom sequence generators (M-sequences) loaded with low-pass filters can be used as a noise generator 4, the output of which is connected to the information input of an amplifier with an adjustable gain of 3. The sequence repetition period should be much longer than the time taken to measure the statistical characteristics of the analyzed process. The variable gain amplifier 3 is a low noise amplifier with a stabilized gain factor, loaded with a linear, electrically controlled attenuator. The recorder 17 can be made on the basis of a specialized programmable microcalculator Electronics MK 64, in which asynchronous reception and processing of analog information is possible in the Working with WU mode through seven channels and outputting information to both the built-in indicator and digital codes to an external device (see Technical description and operating instructions for microcalculator Electronics MK 64). The recorder 17 digitizes and processes the digital samples of the signals arriving at its inputs using the processing program recorded in a special memory and displays the measured statistical characteristics: dispersion, third and fourth cumulants, asymmetry coefficients and kurtosis.

The device operates as follows. Analyzed centered stationary process X (t) and reference centered stationary Gaussian noise coming from the noise generator

4 through the amplifier with adjustable gain 3, alternately, for half the period of the clock frequency, are fed by the switch 1 to the input of the amplifier with

changing the sign of the gain 2. The control signal from the output of the clock divider 6 through each period of the clock frequency changes the sign of the gain of the amplifier 2.

each time the polarity of the process being analyzed and the reference noise change, and therefore, the sign of the asymmetry coefficient of the process being analyzed changes. Gaussian noise has an asymmetry coefficient

equal to zero. The resulting oscillation after the adder 3, where it is endowed with a constant component, is fed to the input of the first quadrator 8. The total power of the signals output from the first quadrator 8 to

one of the periods of the clock frequency can be written as follows:

for the analyzed process:

25

P + L / 4U -t W3X (Dx + + Dy) + 2 (DX + Dy) 2 + (Dx + Dy) +, (4) for the reference Gaussian noise:

thirty

P + 4uWay + 4tT (Dy + Dr) + + 2 (Dy + Dr) 2 + (Dy + D,) +, (5)

where: in expressions, the last terms in square brackets are the powers of the constant components. Their difference is determined by the expression:

dP A2 (Dx-Dr).

In the next period of the clock frequency, the expressions for the total powers differ only in the sign of the third cumulative L / s of the analyzed process. From the output signal of the first quad 8 synchronous

By detecting with the first multiplication unit 10 and the first centering filter 13, a DC component difference signal is proportional to the difference between the variances of the analyzed process and the reference noise. After amplification in the voltage amplifier 16, this signal in the feedback circuit changes the gain of the amplifier with an adjustable gain of 3 to those

until the variance is ensured

Dx Dr.

In this case, the difference in the total signal powers at the output of the first quadrator 8 is determined by the expression:

dP A2 (W / jx + 4uW3x),

and is different in adjacent periods of the clock frequency due to a change in sign with the third cumulant of the analyzed process. The constant component of the output of the second quadrator 9 is proportional to the total power of the signals output of the first quadrator 9. From this component, the component of the total power difference 4A is extracted from the second multiplication unit 11, the second centering filter 14 and the clock frequency oscillation. and L / sx, is proportional to the fourth cumulant of the analyzed process, Similarly, by synchronous detection using the third block. Multiplication 12, the third centering filter 15 and the divider signal a component of the total power difference is proportional to the third cumulant of the analyzed process. These voltages, together with the signal from the output of the voltage amplifier 16, which is proportional to the variance of the analyzed process, are fed to the registration inputs of the recorder 17. After digitalizing, the digital samples of the signals are used to determine the variance estimates, the third and fourth cumulants, and the asymmetry and kurtosis coefficients . The recorder 17 displays the obtained estimates of the statistical characteristics of the analyzed process or provides their values to the consumer in digital form.

The expansion of the functionality of the proposed device is achieved both due to the fact that simultaneously with the dispersion and kurtosis coefficient, the third and fourth cumulants are measured, and due to the appearance of the possibility of determining the asymmetry coefficient based on the third cumulant and, as a result, a more reliable classification the analyzed process. Moreover, the measurement of cumulants makes it possible to classify the processes, even if they arrive at the input of the device together with an additive Gaussian noise, in particular, having a dispersion drift. In known devices, it is impossible to determine the true probabilistic characteristics of the analyzed process in this case. Use of cumulants of the one-dimensional density of the spread distribution

The tea process is more convenient for the operational classification of processes than for moments (including normalized central ones), as well as for comparison with Gaussian noise. If the analyzed process is Gaussian, then all its higher cumulants are equal to zero, in contrast to even moments. Therefore, the analysis of deviations from the Gaussian law can be done with

0 less instrumental error. The knowledge of the cumulants of the probabilistic distribution of the process makes it possible to honestly assess the degree of deviation of the distribution law from the Gaussian one.

Claims (1)

5 Claims A device for determining the statistical characteristics of random processes, comprising a first quadrator, a first and second centering filters, an amplifier with 0 adjustable gain, an amplifier with a variable sign of the gain, a voltage amplifier, a first multiplication unit, a switch and a clock generator, the output being 5 of the first quadrator is connected to the input of the first factor of the first multiplication unit, the output of the first centering filter is connected to the input of the voltage amplifier, the output of which is connected to the reference input 0 values of the gain of the amplifier with an adjustable gain, the output of which is connected to the first information input of the switch, the control input of which is connected to the output of the clock generator, characterized in that, in order to expand the functionality of the device by measuring the third and fourth cumulants and determining the coefficient Asymmetry, it introduces a noise generator, adder, second and third multiplication units, a second quadrator, a third centering filter, a registrar and a frequency divider, the output of the noise generator being connected to the information input of an amplifier with a controlled gain, the output of a voltage amplifier is connected to the registrar dispersion registration input, the output of the first block is multiplied: 0 is not connected to the input of the first centering filter, the input of the second factor of the first block of multiplication is combined with the input of the first factor of the second block of multiplication, with the input of the frequency divider 5 is connected to the output of the clock generator, the output of the first quadrator is connected to the input of the second quadrator, the output of which is connected to the input of the second factor of the second multiplication unit and the input of the first factor of the third unit is multiplied, the input of the second factor of the third multiplication unit is combined with the input of the sign of the amplifier with a variable a gain coefficient sign and is connected to the output of the frequency divider, the outputs of the second and third multiplication units are connected, respectively, through the second and third centering filters register respectively with the inputs of the fourth and third cumulative ntov registrar input of the first 0 a quad is connected to the output of the adder. the first input of which is the input of the reference voltage setting of the device, the second input of which is connected to the output of the amplifier with a variable sign of the gain, the information input of which is connected to the output of the switch, the second information input of which is the information input of the device.