RU2738602C1 - Method for simultaneous measurement of frequency, phase, initial phase and harmonic signal amplitude - Google Patents

Abstract

FIELD: measurement.

SUBSTANCE: method relates to measurement equipment and can be used for simultaneous measurement of frequency, phase, initial phase and amplitude of a continuous harmonic signal based on a set of initial data specified by a large set of discrete readings. Disclosed method comprises discretising an analogue signal, representing a fragment thereof with a triplet of digital codes S₁, S₂, S₃, formed at moments of time t₁, t₂, t₃, is characterized by that the signal representation is generated by a large set of digital codes S_i formed at corresponding time instants t_i, where i is from 4 to N, where N is much more than four, is a row of natural numbers limited by formed set of counts of digital codes, with equal sampling interval of digital codes counts Δt, used for simultaneous determination of signal frequency, initial signal phase, signal phase, signal amplitude.

EFFECT: technical result consists in improvement of accuracy of simultaneous measurement of frequency, phase, initial phase and amplitude of harmonic signal, in the presence of errors in measurement of amplitude in used counts.

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Description

The method relates to measuring equipment and can be used for simultaneous measurement of frequency, phase, initial phase and amplitude of a continuous harmonic signal from a set of initial data given by a large set of discrete samples.

There is a known method for determining the frequency of a narrow-band signal (see patent RU 2117306, published on 08/10/1998), which consists in sampling the signal, calculating its spectrum, determining the number of the maximum spectral component, measuring its amplitude, as well as the amplitude and number of the largest of the adjacent components, and using this raw data to calculate the frequency.

A known method for measuring the amplitudes of harmonic oscillations (see patent RU 2060475, published on April 15, 1993), which consists in registering in the spectrum of the signal harmonics with the maximum amplitude, determining its frequency and using this frequency in the formula for calculating the amplitude of harmonic oscillations.

A known method of joint measurement of frequency, amplitude, phase and initial phase of a harmonic signal (see patent RU 2486529, published on June 27, 2013), which is selected as a prototype, consists in sampling an analog signal, representing its fragment with a triple digital code S ₁ , S ₂ , S ₃ , generated at times t ₁ , t ₂ , t ₃ and used to calculate the frequency of the signal f. In this case, the signal fragment and the corresponding triple of codes are selected so that the S ₂ code is not equal to zero. When measuring frequency, the same codes are used to calculate the amplitude U, the phase ϕ and the initial phase of the signal ϕ ₀ .

, где τ - интервал дискретизации; при этом фрагмент сигнала и соответствующую ему тройку кодов выбирают так, чтобы код S₂ не равнялся нулю, одновременно с измерением частоты, те же коды используют для вычисления амплитуды U, фазы ϕ и начальной фазы сигнала ϕ₀ в соответствии с выражениями:

где фаза ϕ соответствует моменту времени t₂.The method is carried out as follows. The received analog signal is sampled, and its fragment, represented by a triplet of digital codes S ₁ , S ₂ , S ₃ , formed at times t ₁ , t ₂ , t _{3 is} used to calculate the signal frequency by the formula

, where τ is the sampling interval; the fragment of the signal and the corresponding triple of codes are selected so that the code S _{2 is} not equal to zero, simultaneously with the measurement of the frequency, the same codes are used to calculate the amplitude U, phase ϕ and the initial phase of the signal ϕ ₀ in accordance with the expressions:

where the phase ϕ corresponds to the time t ₂ .

The disadvantage of this method is the low accuracy of simultaneous measurement of frequency, phase, initial phase and amplitude of a continuous harmonic signal.

The technical problem lies in the insufficient accuracy of simultaneous measurement of frequency, phase, initial phase and amplitude of a continuous harmonic signal in the presence of errors in measuring the amplitude in the samples used.

The technical problem (technical result) to be solved for the method of simultaneous measurement of the frequency, phase, initial phase and amplitude of a harmonic signal is to increase the accuracy of measuring the frequency, phase, initial phase and amplitude of a harmonic signal, in the presence of errors in measuring the amplitude in the samples used.

The technical problem to be solved (technical result) in the method of simultaneous measurement of frequency, phase, initial phase and amplitude of a harmonic signal, including sampling of an analog signal, representation of its fragment by three digital codes S ₁ , S ₂ , S ₃ , formed at times t ₁ , t ₂ , t ₃ , is achieved by the fact that the signal representation is formed by a large set of digital codes S _i formed at the corresponding time moments t _i , where i is from 4 to N, where N is much more than four, is a series of natural numbers limited by the formed set of samples digital codes, with an equal sampling interval of samples of digital codes Δt, used to simultaneously determine the frequency of the signal ω according to the formula:

- производная первого порядка значения цифрового кода i-го отсчета;

- производная второго порядка значения цифрового кода i-го отсчета; avg - операция вычисления среднего арифметического набора значений, начальной фазы сигнала ϕ₀ по формуле:where k is the order of approximation accuracy; N is the number of samples of digital codes; i is the count number;

- derivative of the first order of the value of the digital code of the i-th sample;

- second order derivative of the value of the digital code of the i-th sample; avg is the operation of calculating the arithmetic mean of a set of values, the initial phase of the signal ϕ ₀ according to the formula:

- производная второго порядка значения цифрового кода i-го отсчета; t₁ - момент времени i-го отсчета; avg - операция вычисления среднего арифметического набора значений, фазы сигнала ϕ_i по формуле:where k is the order of approximation accuracy; N is the number of samples of digital codes; i is the count number; ω is the signal frequency; S _i - value of the digital code of the i-th sample;

- second order derivative of the value of the digital code of the i-th sample; t ₁ - time of the i-th sample; avg is the operation of calculating the arithmetic mean of a set of values, the phase of the signal ϕ _i by the formula:

- производная второго порядка значения цифрового кода i-го отсчета; t_i - момент времени i-го отсчета, амплитуды сигнала U по формуле:where i is the count number; ω is the signal frequency; S _i - value of the digital code of the i-th sample;

- second order derivative of the value of the digital code of the i-th sample; t _i is the moment of time of the i-th sample, the amplitude of the signal U according to the formula:

- производная первого порядка значения цифрового кода i-го отсчета; t_i - момент времени i-го отсчета; avg - операция вычисления среднего арифметического набора значений, с учетом шумовой составляющей сигнала, где оценки производных отсчетов значений цифровых кодов

вычисляются в моменты времени t_i (i=k, N-k) методом центральных конечных разностей с использованием формул аппроксимации k-го порядка точности при условии, что количество отсчетов цифровых кодов N много больше порядка точности аппроксимации k.where k is the order of approximation accuracy; N is the number of samples of digital codes; i is the count number; ω is the signal frequency; ϕ is the phase of the signal;

- derivative of the first order of the value of the digital code of the i-th sample; t _i - time of the i-th sample; avg - the operation of calculating the arithmetic mean of a set of values, taking into account the noise component of the signal, where estimates of the derivatives of the samples of the values of digital codes

are calculated at times t _i (i = k, Nk) by the method of central finite differences using approximation formulas of the kth order of accuracy, provided that the number of samples of digital codes N is much greater than the order of accuracy of approximation k.

FIG. 1 shows a block diagram of a device that implements the proposed method for simultaneous measurement of frequency, phase, initial phase and amplitude of a harmonic signal.

FIG. 2 shows the algorithm of the controller for measuring the parameters of a harmonic signal.

A device for implementing the proposed method for simultaneous measurement of frequency, phase, initial phase and amplitude of a harmonic signal, shown in FIG. 1 contains a narrowband optical signal source 1, a Mach-Zehnder modulator 2, connected in series by fiber optic fibers, while the electrical port of the Mach-Zehnder modulator 2 is an input of the device, a photodetector 3, and a controller for measuring parameters of a harmonic signal 4, while a controller for measuring parameters of a harmonic signal 4 has an output, which is the output of the device.

Beforehand, a program is loaded into the controller unit for measuring the parameters of a harmonic signal 4, which operates according to the algorithm shown in FIG. 2.

Connect the power supply system for the units of the source of the narrow-band optical signal 1, the Mach-Zehnder modulator 2, the controller for measuring the parameters of the harmonic signal 4.

The power supply system necessary for the blocks of the source of the narrowband optical signal 1, the Mach-Zehnder modulator 2, the controller for measuring the parameters of the harmonic signal 4 in FIG. 1 is not shown.

The device works as follows. A harmonic signal with measured parameters is supplied to the electrical port of the Mach-Zehnder 2 modulator, for example, from the receiving antenna.

For simultaneous measurement of frequency, phase, initial phase and harmonic signal amplitude using the narrowband optical signal 1 generates a signal with a frequency ƒ _1, which is then modulated in the modulator is a Mach-Zehnder interferometer 2, operating in a zero operating point of the modulation characteristic for carrier suppression, measured harmonic signal with unknown parameters ƒ _m . The resulting pair of harmonics with frequencies ƒ ₁ -ƒ _m and ƒ ₁ + ƒ _{m is} fed to the photodetector 3, where the beat of this pair of harmonics S is formed. The resulting beat is fed to the controller for measuring the parameters of the harmonic signal 4, where the signal is sampled and the frequency is measured, phase, initial phase and amplitude of the harmonic signal fed to the electrical port of the Mach-Zehnder modulator 2.

Consider the implementation of a method for simultaneous measurement of frequency, phase, initial phase and amplitude of a harmonic signal.

The analog signal is sampled. The obtained set of samples of digital codes {S _i } i = 1, N (where N >> 4) (signal amplitude) measured at times t _{i is} used for further simultaneous determination of the frequency, phase, initial phase and amplitude of the harmonic signal. Before starting the controller for measuring the parameters of a harmonic signal with a given algorithm, the required errors in calculating the frequency, initial phase and amplitude are set - ε _ω , ε _ϕ , ε _U , respectively. The initial value k = 0 of the order of accuracy of approximation of finite differences is set. Further calculations are carried out according to the following cyclic algorithm.

для всех значений номеров отсчетов i ∈ [k, N-k]. Вычисляют значение ω_i для всех значений номеров отсчетов i ∈ [k, N-k]. По известным данным ω_i вычисляются значения ϕ_i для всех значений номеров отсчетов i ∈ [k, N-k]. По известным данным ω_i и ϕ_i вычисляются значения значение U_i для всех значений номеров отсчетов i ∈ [k, N-k], Вычисляются средние значения ω^k _i, ϕ^k _i и U^k _i. Для k>1 проверяется погрешность вычисления частоты, начальной фазы и амплитуды, в противном случае происходит переход к началу алгоритма. Если одновременно не выполняются условия требуемой точности для вычислений частоты, начальной фазы и амплитуды |ω^k-ω^k-1|<ε_ω и |ϕ₀ ^k-ϕ₀ ^k-1|<ε_ϕ и |U^k-U^k-1|<ε_U, то осуществляется переход на начало алгоритма. В случае выполнения требований необходимой точности вычислений, осуществляется выход из цикла с присвоением значений вычисленных частоты, начальной фазы, мгновенной фазы и амплитуды ω=ω^k, ϕ₀=ϕ^k ₀, ϕ_i=ϕ^k _i, U=U^k, соответственно. Производится расчет шумовой составляющей сигнала S_i ^Noise=Ucos(ωt+ϕ_i)-S_i для всех номеров отсчетов i ∈ [1,N]. Производится вывод полученных результатов, частоты, начальной фазы и амплитуды - ω, ϕ₀, U соответственно, кроме того, выводятся значения мгновенной фазы ϕ_i и шумовой составляющей сигнала S_i ^Noise для номеров отсчетов i ∈ [1,N].The value k = k + 1 is set to increase the order of accuracy of the approximation of finite differences. By the formulas for the central finite differences of the k-th order of approximation accuracy, the numerical values of the derivatives of digital codes are calculated

for all values of the numbers of samples i ∈ [k, Nk]. The value of ω _{i is} calculated for all values of the numbers of samples i ∈ [k, Nk]. According to known data ω _i φ _i values are calculated for all values of samples numbers i ∈ [k, Nk]. According to known data ω _i and φ _i are calculated importance value U _i for all i ∈ numbers of samples [k, Nk] values, calculates an average value ω ^k _i, φ ^k _i and U ^k _i. For k> 1, the error in calculating the frequency, initial phase and amplitude is checked; otherwise, the transition to the beginning of the algorithm occurs. If the conditions of the required accuracy for calculating the frequency, initial phase and amplitude are not simultaneously satisfied | ω ^k -ω ^k-1 | <ε _ω and | ϕ ₀ ^k -ϕ ₀ ^k-1 | <ε _ϕ and | U ^k -U ^{k- 1} | <ε _U , then the transition to the beginning of the algorithm is carried out. If the requirements for the required accuracy of calculations are met, the loop is exited with the assignment of the values of the calculated frequency, initial phase, instantaneous phase and amplitude ω = ω ^k , ϕ ₀ = ϕ ^k ₀ , ϕ _i = ϕ ^k _i , U = U ^k , respectively ... The calculation of the noise component of the signal S _i ^Noise = Ucos (ωt + ϕ _i ) -S _i for all numbers of samples i ∈ [1, N] is performed. The output of the obtained results, frequency, initial phase and amplitude - ω, ϕ ₀ , U, respectively, is carried out, in addition, the values of the instantaneous phase ϕ _i and the noise component of the signal S _i ^Noise for the numbers of samples i ∈ [1, N] are displayed.

A device for implementing the proposed method for simultaneous measurement of frequency, phase, initial phase and amplitude of a harmonic signal can be implemented on the following elements designed to operate at a wavelength of 1300 nm (other wavelengths are also possible), for example:

The laser diode IDL10S-1300 NII "Polyus" or DMP0131-22 LLC NPF "Dilaz" can be selected as a source of a narrow-band optical signal 1;

As the Mach-Zehnder 2 modulator, a modulator based on the Laser2000 Mach-Zehnder interferometer 500-x-13 can be selected;

As the photodetector 3, a high-speed fiber-optic InGaAs microwave broadband PIN photodetector from Optilab, for example, PD-40-MM, can be selected;

As a controller for measuring the parameters of a harmonic signal 4, a microprocessor controller based on chips from Atmel, Microchip, etc .;

Reference cords or TELECOM-TEST cables from SOKOL Production and Trade Company LLC can be selected as fiber light guides.

To build a device for implementing the proposed method for simultaneous measurement of frequency, phase, initial phase and amplitude of a harmonic signal, all of these units for generating, receiving and processing signals can be performed on a single crystal or in an integrated design.

All this allows us to speak about the achievement of a solution to the technical problem (technical result) - simultaneous measurement of frequency, phase, initial phase and amplitude of a harmonic signal, in the presence of errors in measuring the amplitude in the samples used.

Claims (33)

A method for the simultaneous measurement of frequency, phase, initial phase and amplitude of a harmonic signal, including sampling an analog signal, representing its fragment with a triple digital code S ₁ , S ₂ , S ₃ , formed at times t ₁ , t ₂ , t ₃ , characterized in that that the signal representation is formed

a set of digital codes S _i , formed at the corresponding times t _i , where i is from 4 to N, where N is much more than four, is a series of natural numbers, limited by a formed set of digital code samples, with an equal sampling interval of digital code samples Δt used for the simultaneous determination of the signal frequency ω by the formula:

where k is the order of approximation accuracy; N is the number of samples of digital codes; i is the count number;

- derivative of the first order of the value of the digital code of the i-th sample;

- second order derivative of the value of the digital code of the i-th sample; avg is the operation of calculating the arithmetic mean of a set of values, the initial phase of the signal ϕ ₀ according to the formula:

where k is the order of approximation accuracy; N is the number of samples of digital codes; i is the count number; ω is the signal frequency; S _i - value of the digital code of the i-th sample;

- second order derivative of the value of the digital code of the i-th sample; t _i - time of the i-th sample; avg is the operation of calculating the arithmetic mean of a set of values, the phase of the signal ϕ _i by the formula:

where i is the count number; ω is the signal frequency; S _i - value of the digital code of the i-th sample;

- second order derivative of the value of the digital code of the i-th sample; t _i - time of the i-th sample, signal amplitude U according to the formula:

where k is the order of approximation accuracy; N is the number of samples of digital codes; i is the count number; ω is the signal frequency; ϕ is the phase of the signal;

- derivative of the first order of the value of the digital code of the i-th sample; t _i - time of the i-th sample; avg - the operation of calculating the arithmetic mean of a set of values, taking into account the noise component of the signal, where estimates of the derivatives of the samples of the values of digital codes

are calculated at times t _i (i = k, Nk) by the method of central finite differences using approximation formulas of the kth order of accuracy, provided that the number of samples of digital codes N is much greater than the order of accuracy of approximation k.

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