RU2654945C1 - Digital method of measuring phase of harmonic signal - Google Patents

Abstract

FIELD: measurement technology; physics.

SUBSTANCE: digital method for measuring phase of harmonic signal makes it possible to simplify the realization of determination of phase of a harmonic signal and to improve the accuracy of the phase determination when the original signal is noisy. Method is based on receiving the primary signal x(t) followed by analog-to-digital conversion using two analog-to-digital converters (ADCs) at two different frequencies. As a result, we get two number arrays y1[i], i=1…K and y2[i], i=1…K-d, where K and K-d are the number of samples of the first and second ADCs, respectively, in measurement interval T, d>1. We select for further processing one of these arrays, which will represent the secondary signal obtained as a result of sampling the primary signal with a frequency below the Nyquist frequency. We calculate with a fast Fourier transform the approximate integer value of the number of periods kp0 of the secondary signal. Create M*N reference signals in range of the number of periods kp2(p)=kp0-1+p*2/N, N – number of steps to search for the number of periods of the secondary signal and phase ϕ2(j)=-π/2+j*27π/M, M is the number of steps to search for the phase value of the secondary signal. We calculate the sums of squared deviations of the secondary source and reference signals for each value of p: ssd(j), j=1…M. We find the minimum values ssd(j); j=1:M, and the value of jmin corresponding to the condition ssd(jmin)=min(ssd(j)), j=1:M each value of p, calculate the current values of the phase function ϕ_result(p)=-π/2+jmin*2π/M, p=1…N. Find the values min(ϕ_result(p)), p=1:N, and the value of pmin corresponding to the condition ϕ_result (pmin)=min(ϕ_result(p)), p=1:M, calculate the total phase value ϕ_res=ϕ_result(pmin), calculate the resulting phase value ϕ_out=ϕ_res or ϕ_out=π-ϕ_res, if abs(ϕ_res)>π/2.

EFFECT: technical result in the realization of claimed method is simplification of the method implementation and an increase in the accuracy of the phase detection with noisy initial signal.

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Description

The invention relates to the field of measurement technology and can be used in radar to determine the phase of a harmonic signal during phase direction finding of an object, as well as in navigation systems, in radio and sonar, in space technologies, in interferometers, in geodesy.

The well-known "Digital method and device for determining the instantaneous phase of the adopted implementation of a harmonic or quasi-harmonic signal." [RU patent No. 2463701]. The principle of determining the phase of the signal is based on the processing of the registered signal fragment

U _ave = Asin (ωt + φ) and the quadrature component generated

U _q = Asin (ωt + ϕ + π / 2) = Acos (ωt + ϕ)

The phase of the signal is determined for time T ₀ . To do this, measure the signal value and the quadrature component at times T ₀ , T0-t and T ₀ + t, t <T ₀ . Next, determine the parameters U _pr- , U _{pr +} , calculate S _pr = U _pr- + U _{pr +} , R _pr = G _pr- -U _{pr +} , where Snp and Rnp are the sum and difference of the instantaneous signal values equally spaced from T ₀ , respectively determine U _sq- , U _{sq +} , calculate S _sq = U _sq- + U _{sq +} , R _sq = U _sq -U _sq , where Sq and Rq - are the sum and difference of the quadrature components of the signal equally spaced from T ₀ , respectively, calculate relations Spr / Sqr and Rkv / Rpr and get the phase value of the signal at point T ₀ :

ωT ₀ + ϕ = arctan (S _pr / S _q );

ωT ₀ + ϕ = -arctg (R _q / R _pr ).

The disadvantage of this method is that even with a slight noise of the signal, the determination of the exact phase value is impossible.

If the signal is noisy, which is typical for phase direction finding systems of objects, the maximum error in determining the phase can reach 100 deg., I.e. in fact, determining the phase (or phase difference) in this way is impossible.

The well-known "Method for joint measurement of frequency, amplitude and initial phase of a harmonic signal", selected for the prototype [RU patent No. 2486529]. The method includes the analog signal sampling, Introduction fragment thereof three digital values S _1, S _2, S _3, formed at the times t _1, t _2, t _3, corresponding to three successive samples, and computing the frequency, amplitude, phase, at time time t ₂ and the initial phase according to the formulas:

To implement this method, it is necessary that the above three samples belong to the same signal period. Phase direction finding systems should work with signals at frequencies up to 40 GHz, therefore, when using the known method, it is required to use an analog-to-digital converter with a sampling frequency above 80 GHz, which is technically very difficult [Koltsov Yu.V. Industrial ultra-high-speed signal converters: ADC and DAC // Advances in modern radio electronics. - 2016. - No. 1. - S. 64-77].

The disadvantage of this method is that the sampling frequency of the signal during measurement must exceed the Nyquist frequency, i.e. more than double the frequency of the original signal, which leads to the complexity of the technical implementation of the method. If the signal is noisy, which is typical for phase direction finding systems of objects, the maximum error in determining the phase can reach 100 deg, i.e. in fact, phase determination in phase direction finding systems with acceptable accuracy by this method is impossible.

The technical problem is to simplify the implementation of the method for determining the phase of a harmonic signal and to increase the accuracy of determining the phase with noisy source signal.

To solve this problem, a digital method for measuring the phase of a harmonic signal is proposed, which includes receiving the primary signal x (t) followed by analog-to-digital conversion using two analog-to-digital converters (ADCs) at two different frequencies, which can be less than the Nyquist frequency. Obtaining two numerical arrays y1 [i], i = 1 ... K and y2 [i], i = 1 ... K-d, where K and K-d are the number of samples of the first and second ADCs, respectively, on the measurement interval T, d> 1. We select one of these arrays for further processing: y1 [i] if max (y1) - min (y1)> max (y2) -min (y2), or y2 [i] if max (y1) - min (y1 ) <max (y2) - min (y2), as a result of which a numerical array y [i] will be generated, representing the secondary signal obtained by sampling the primary signal with a frequency below the Nyquist frequency. Using the fast Fourier transform, we calculate the approximate integer value of the number of periods kp0 of the secondary signal y [i]. We create M * N reference signals in the region of the number of periods kp2 (p) = kp0-1 + p * 2 / N, N is the number of search steps for the number of periods of the secondary signal and phase ϕ2 (j) = - π / 2 + j * 2π / M, M - the number of steps to search for the phase value of the secondary signal. We calculate the sum of the squared deviations ssd (j), j = 1 ... M of the secondary source and reference signals for each value of p.

We find the minimum values of the squared deviations ssd (j); j = 1: M, and the values of jmin corresponding to the condition ssd (jmin) = min (ssd (j)), j = 1: M for each value of p and for each p we calculate the current values of the phase function ϕ _{_} result (p) = -π / 2 + jmin * 2π / M, p = 1 ... N. We find the values minϕ_result (p)), p = 1: N, and the value pmin corresponding to the condition ϕ_result (pmin) = min (ϕ_result (p)), p = 1: M. We calculate the total value of the phase ϕ_res = ϕ_result (pmin), and the resulting value of the phase ϕ_out = ϕ_res or ϕ_out = π-ϕ_res, if abs (ϕ_res)> π / 2.

Distinctive essential features of the proposed digital method is the sampling of the original signal using two analog-to-digital converters at two different frequencies and the digital processing of these signals, as a result of which the phase of the signal can be determined with a given accuracy at a frequency of samples made at a frequency below the Nyquist frequency and with noise signal.

The idea of the proposed digital method for measuring the phase of the signal is that the phase of the secondary signal obtained from sampling at a frequency lower than the Nyquist frequency is exactly equal to the phase of the original signal or is shifted by π, despite the fact that the frequency of the secondary signal is less than the frequency of the original, which leads to simplify the implementation of the method for determining the phase of the harmonic signal. When choosing the search area for the phase value, we proceed from the fact that in phase direction finding systems the phase value is in the range [-π / 2 + π / 2]. Thanks to the proposed algorithm, the phase is determined by the first secondary signal, and if the number of samples turns out to be a multiple of the number of periods of the original signal and the secondary signal loses its oscillatory character and degenerates into a straight line, which excludes the possibility of determining the phase, an automatic transition to processing the second secondary signal . In addition, the search for the phase of the secondary signal is performed in the region [-0.5π 1.5π], which ensures obtaining the phase value both in the case when there is no phase shift by π, and in the case when there is a bias, to take into account the possible phase shift of the secondary signal relative to the phase of the primary signal, the true value of the phase of the signal is calculated as ϕ_res = π-ϕ_res if abs (ϕ_res)> π / 2, where ϕ_res is the obtained phase value without taking into account the possible phase shift of the secondary signal. The error in determining the phase depends on the number of samples of the signal kt, the noise level of the signal, and on the dimension M * N of the search region for the number of periods of the secondary signal and phase and can be made arbitrarily small, which will provide an increase in the accuracy of determining the phase of the proposed method when the signal is noisy. Thus, a set of distinctive features is necessary and sufficient to solve the problem.

FIG. 1 and FIG. 2 illustrate the effect of sampling at a frequency lower than the Nyquist frequency: the original signal is shown in FIG. 1, a secondary signal of a lower frequency, obtained as a result of sampling with a frequency lower than the Nyquist frequency, is shown in FIG. 2.

A diagram of a device for the possible implementation of the proposed digital method of measuring the phase of the signal [Fig. 3]. The device includes: 1 - a clock generator SI1, SI2 and SI3, 2 - a signal source, 3 and 4 - analog-to-digital converters, 5 and 6 - address counters of random access memory (RAM), 7 and 8 - RAM, 9 - calculator . In FIG. 4 shows the timing diagram of the clock pulses SI1, SI2 and SI3. Figure 5 shows a typical graph of the function of the sum of the squares of the deviations of the secondary source and reference signals ssd (j, p), j = 1: M, p = 1 ... N.

An example implementation of the proposed digital method in the device is shown in FIG. 3.

The clock generator 1 generates a clock pulse SI1, which resets the counters 5 and 6 of the write address in RAM1 and RAM2. From the moment the SI1 clock pulse is generated, the generation of SI2 and SI3 clock pulses by the generator 1 begins, analog-to-digital conversion of the primary harmonic input signal x (t), having, for example, a frequency of 5000 MHz, with a number of periods of 1000, an amplitude equal to unity, the mean square noise value 0.05 and an initial phase of 0.8 radians, using analog-to-digital converters 3 and 4, at a sampling frequency of the signal, for example, 1000 MHz, the number of sampled values of the signal 200 at converter 3 and the dis signal retrieval at 940 MHz and the number of sampled values of signal 188 at converter 4, recording the results of conversion to random access memory 7 and 8 at the addresses specified by address counters 5 and 6. At the same time, 200 discrete samples of the signal will be recorded in RAM 7, and in RAM 8 -200-2 = 188 discrete samples of the signal. Next, the calculator 6 reads and processes the sampled signals recorded and stored in the random access memory 7 and 8 in accordance with the algorithm described below. Processing actions are performed in the following order:

1. Read the input primary signal recorded in random access memory 7 and 8, presented in the form of two numerical arrays: y1 [i], i = 1 ... K, K = 200 and y2 [i], i = 1 ... Kd, K = 200, d = 2, respectively.

2. Form the array y [i] according to the rule: y [i] = y1 [i] if max (y1) -min (y1)> max (у2) -min (y2), or y [i] = y2 [ i] if max (y1) -min (y1) <max (y2) -min (y2). In this case, the value max (y1) - min (y1) will be close to zero, due to the fact that the number of discrete samples 200 is a multiple of the number of periods 1000, and the value max (у2) -min (y2) will be approximately equal to the amplitude of the original signal x (t). Therefore, y2 [i] will be taken as an array of the secondary signal y [i]. (If the number of discrete samples of converters 3 and 4 were not a multiple of the number of periods 1000, then y1 [i] and y2 [i] could be taken as an array of the secondary signal).

3. Fast Fourier transform of the numerical array y [i] of the secondary signal is performed, as a result of which an array of the frequency spectrum of the secondary signal is formed in the form of a set of K or K-d numbers (in this case, a set of K-d, ie 188).

4. Determine the element number kp0 of the array of the frequency spectrum, which corresponds to the maximum value. This number kp0 is a rough estimate of the number of periods of the secondary signal (in this case, kp0 = 10).

5. Create M * N reference harmonic signals with the number of periods kp2 (p) = kp0-1 + p * 2 / N and phase ϕ2 (j) = - π / 2 + j * 2π / M, for example, M = 200, N = 200.

6. Calculate the sum of the squared deviations ssd (j), j = 1 ... M of the secondary source and reference signals for each value of p.

7. Find the minimum value ssd (j), j = 1: M and the value jmin corresponding to the condition ssd (jmin) = min (ssd (j)), j = 1: M for each value of p.

8. The current values of the phase function for each value of p are calculated: ϕ_result (p) = - π / 2 + jmin * 2π / M, p = 1 ... N.

9. Find the values min (ϕ_result (p)), p = 1: N and pmin values corresponding to the condition ϕ_result (pmin) = min (ϕ_result (p)), p = 1: N.

10. The total phase value ϕ_res = ϕ_result (pmin) is calculated. In this case, ϕ_res = 0.7992. The jmin and pmin thus obtained correspond to the absolute minimum of the function ssd (j, p), the graph of which is shown in FIG. 5.

11. The resulting phase value ϕ_out = ϕ_res is calculated if abs (ϕ_res) <π // 2 or ϕ_res = π-ϕ_res if abs (ϕ_res)> π // 2. In this case, abs (ϕ_res) <π // 2; therefore, ϕ_out = ϕ_res = 0.7992. A typical error in determining the phase in radians will be 0.8 - 0.7992 = 0.0018 rad., In degrees - 0.0456 degrees.

Thus, the simplification of the implementation of the method for determining the phase of the harmonic signal was achieved due to the fact that the signal was sampled using the ADC at a frequency of 1 GHz instead of 10 GHz that would be necessary in the prototype. The increase in the accuracy of phase determination with noisy source signal is confirmed by the fact that according to the results of 1000 statistical tests, the maximum error in determining the phase of the proposed method is 1.76 degrees, mean square - 0.49 degrees, which is significantly less than in the prototype: 100 degrees, and 8.5 degrees, respectively.

Claims (1)

A digital method for measuring the phase of a harmonic signal, including sampling the analog signal and calculating the phase of the signal from several samples, characterized in that the signal is recorded using two analog-to-digital converters operating at two different frequencies, while receiving numerical arrays of secondary signals y1 [i ], i = 1 ... K and y2 [i], i = 1 ... Kd, d> 1, from which the array y [i] is formed: y [i] = y1 [i] if max (y1 ) - min (y1)> max (y2) - min (y2), or y [i] = y2 [i], if max (y1) - min (y1) <max (y2) - min (y2), produce Fourier transform of a numerical array y [i] secondary with drove, after which they form an array of the frequency spectrum of the secondary signal in the form of a set of K or Kd numbers, determine the element number kp0 of the array of the frequency spectrum, which corresponds to the maximum value, which is a rough estimate of the number of periods of the secondary signal, create M * N reference harmonic signals with the number of periods kp2 (p) = kp0-1 + p * 2 / N and phase ϕ2 (j) = - π / 2 + j * 2π / M, the sum of the squared deviations ssd (j), j = 1 ... M of the secondary and a reference signal for each p, find the values jmin corresponding to the condition ssd (jmin) = min (ssd (j)), j = 1: M, for each value of p, calculate the current values of the phase function ϕ_result (p) = - π / 2 + jmin * 2π / M, p = 1..N, find the values of pmin corresponding to the condition ϕ_result (pmin) = min (ϕ_result (p)), p = 1: N, and calculate the total value of the phase ϕ_res = ϕ_result (pmin), calculate the resulting value of the phase ϕ_out = ϕ_res if abs (ϕ_res) <π // 2 or ϕ_res = π-ϕ_res if abs (ϕ_res)> π // 2.

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