RU2041496C1 - Device for determination of initial moments of arbitrary order - Google Patents

Abstract

FIELD: computer engineering. SUBSTANCE: device has input terminal 1, functional converter 2, integrator 3, reference voltage source 5, comparator 4, univibrator 6, counters 7, 9, rectangular pulse generator 8, dividing unit 10, indicator 11. This results in possibility to remove error of method of measuring. EFFECT: increased precision. 1 dwg

Description

 The invention relates to computing and information-measuring equipment and can be used to determine the initial moments of any order (including fractional) of a random variable x, as well as any function y of a random argument x y φ (x).

 A device for determining one-dimensional initial moments of the Kth order of a random signal (1), comprising an integrating analog-to-digital converter, a unit for determining the mathematical expectation, reversible counters of control and result, a decimal counter of the moment order, a sampling counter, triggers, AND, OR, NOT, digital-to-analog converter, decoder, display unit, switches.

 The disadvantages of the analogue are the complexity and low accuracy of the device.

 Analogues of the proposed device also include a device for determining one-dimensional initial moments of the Kth order (2), containing a comparison unit, a random signal generator, consisting of a pseudo-random signal generator and a digital-to-analog converter, a clock generator, a counter accumulating an adder, a power converter , display unit, initial conditions setting unit.

 The disadvantage of the analogue is a significant methodological error of the device, due to the algorithm of its operation.

 The closest technical solution to the proposed one is a device for determining the probability distribution of the amplitudes of pulse signals (3), which contains a signal sensor, a single vibrator, a peak detector, a pulse shaper, an amplitude-pulse modulator, counters, an amplitude analyzer, a division unit, and an indicator.

 The disadvantage of the prototype is a significant methodological error due to the algorithm of the device.

 The purpose of the invention is to increase the accuracy of the device due to the use of a new information processing algorithm, which eliminates the methodological error.

 This goal is achieved by the fact that in the device for determining the probability distribution of the amplitudes of pulse signals, containing a single vibrator, two counters, a division unit and an indicator, the input of which is connected to the output of the division unit, the input of which is connected respectively to the outputs of the first and second counters, an additional rectangular generator pulses, functional converter, integrator, comparator and reference voltage source, the output of which is connected to the first input of the comparator, the output of which is connected to a single vibrator, the inverse and direct outputs of which are connected respectively to the counting input of the first counter and to the reset input of the integrator, the output of which is connected to the second input of the comparator, the information input of the device is the input of the functional converter, the output of which is connected to the input of the integrator, the output of the square-wave generator is connected to counting input of the second counter.

 The drawing shows a diagram of the device.

 The device contains an input terminal 1 connected to the input of the functional converter 2, the output of which is connected to the input of the integrator 3, the output of which is connected to the second input of the comparator 4, the first input of which is connected to the output of the reference voltage source 5 (ION), and the output is connected to the input of a single-shot 6, the inverse and direct outputs of which are connected respectively to the counting input of the first counter 7 and to the reset input of the integrator 3, a rectangular pulse generator (GUI) 8, the output of which is connected to the counting input of the second counter and 9, the output of which is connected to the input of the divider of the division unit 10 (DB), the input of which is divisible is connected to the output of the first counter 7, and the output is connected to the input of the indicator 11.

 In the proposed private embodiment of the device, the circuit of the functional converter 2 contains an analog-to-digital converter (ADC) 12, the input of which is the input of the functional converter 2, and the output is connected to the address input of a permanent storage device (ROM) 13, the output of which is connected to the digital input of the digital-to-analog converter (DAC) 14, the input of the reference voltage of which is connected to the output of the additional ION 15, and the output is the output of the functional Converter 2.

 The integrator circuit 3, in particular, contains an input connected through an input resistor 16 with an inverting input of an operational amplifier (op amp) 17 connected to the first output of the discharge resistor 18 and through a capacitor 19 with an output of an op amp 17 connected to the outputs of an integrator 3 and a switch 20, the information input of which is connected to the second output of the discharge resistor 18, and the control input of the switch 20 is connected to the reset input of the integrator 3, the non-inverting input of the OS 17 is connected to the device common bus.

Consider the operation of the device in two applications:
A. The application of the device to determine the initial moments of the initial random process x (t).

x^K(t)dt, (4) где t₁ начальный момент интегрирования;
t₂ конечный момент интегрирования, при котором интеграл u₃достигает единичного значения, задаваемого источником 5 опорного напряжения.At the input terminal 1, the investigated random process x (t) is supplied. At the output of the ADC 12, a digital code appears proportional to the process
K ₁₂ ≡ x (t). (1)
This code is applied to the input of the ROM 13, which in this application of the device is used as a power converter. At the output of the ROM 13, a binary number appears, proportional to the degree "K" of the process x (t), i.e. ROM output code 13 is
K ₁₃ ≡ x ^K (t). (2)
This code is converted using the DAC 14 to voltage
u ₁₄ ≡ x ^K (t). (3)
The output voltage of the DAC 14 is applied to the input of the integrator 3, the output voltage of which varies according to the formula
u ₃ ≡

x ^K (t) dt, (4) where t _{1 is the} initial moment of integration;
t _{2 is the} final moment of integration at which the integral u ₃ reaches the unit value specified by the reference voltage source 5.

When u ₃ u _{5, the} comparator 4 is triggered, starting with its output voltage one-shot 6.

 A short pulse from the direct output of the one-shot 6 acts on the control input of the switch 20, which, when opened, closes the discharge circuit of the capacitor 19 through the resistor 18. Given that the value of the discharge resistor 18 is very small (it is 4 orders of magnitude less than the input resistor 16), the voltage Integrator 3 drops to zero in a few microseconds.

 A short pulse from the inverse output of a single-shot 6 increases by one the contents of the counter 7.

x^K(t)dt (5) и т.д.A similar operation is repeated on the next interval t ₂ t ₃ at which the integral u ₃ again grows from zero to u ₅
u ₃ ≡

x ^K (t) dt (5), etc.

x^K(t)dt, (6) количество которых подсчитывается счетчиком 7.Thus, at time intervals t _i t _{i + 1, the} integrator 3 measures the same quanta of the integral
Δ≡

x ^K (t) dt, (6) the number of which is counted by the counter 7.

x^K(t)dt. (8)
Время усреднения Т может быть определено по формуле
T N₉· T_п8=

(9) где N₉ содержимое второго счетчика 9;
Т_п8 длительность периода импульсов ГПИ 8;
f₈ частота ГПИ 8.The value of each quantum is numerically equal
Δ = U ₅ (7)
As you know, the initial moment of the Kth order is
μ _k =

x ^K (t) dt. (8)
The averaging time T can be determined by the formula
TN ₉ · T _p8 =

(9) where N _{9 is the} contents of the second counter 9;
T _{p8 the} duration of the pulse period GUI 8;
f ₈ frequency GUI 8.

x^K(t)dt= u₅·N₇, (10) где N₇ содержимое первого счетчика 7.The integral over the averaging time T, taking into account formula (8), is equal to

x ^K (t) dt = u ₅ · N ₇ , (10) where N _{7 is the} content of the first counter 7.

·u₅·N₇= u₅f₈

K

(11) где К u₅f₈ постоянный коэффициент пропорциональности.Given formulas 8-10, we can write
μ _kx =

U ₅ N ₇ = u ₅ f ₈

K

(11) where K u ₅ f _{8 is a} constant coefficient of proportionality.

The division unit 10 performs the operation of dividing the number N ₇ by N _{9 the} output code of the database 10 is proportional to the measured moment μ _kx The moment value is continuously displayed on the digital indicator 11.

 B. The application of the device for determining the initial moments of a random process y (t) obtained from the original random process x (t) after conversion in accordance with the formula y φ (x, t).

The device works in the same way as in option A. However, the ROM 13 in this application is used as a functional converter that provides a code at the output of the ROM 13
K ₁₃ ≡ [φ (x)] ^k . (12)
The indicator 11 displays the value of the moment μ _ku
An advantage of the proposed technical solution in comparison with the known ones is its higher accuracy, achieved due to the absence of a methodological error. The circuit of the device is simple, it is implemented on several widely distributed circuits.

Claims (1)

 A device for determining the initial moments of any order, containing a single vibrator, two counters, a division unit and an indicator, the input of which is connected to the output of the division unit, the inputs of which are connected respectively to the outputs of the first and second counters, characterized in that a rectangular pulse generator is inserted into it, a functional a converter, an integrator, a comparator and a reference voltage source, the output of which is connected to the first input of the comparator, the output of which is connected to the input of a single vibrator, inverse and direct output which are connected respectively to the counting input of the first counter and the reset input of the integrator, the output of which is connected to the second input of the comparator, the information input of the device is the input of the functional converter, the output of which is connected to the input of the integrator, the output of the square-wave generator is connected to the counting input of the second counter.