RU2363005C1 - Method of spectral analysis of polyharmonic signals and device to this end - Google Patents

Abstract

FIELD: instrument making.

SUBSTANCE: invention relates to measuring instruments and can be used in discrete analysis of polyharmonic signals, including those that feature fast variations of fundamental frequency. The proposed method consists in that the analyzed signal is fed to the input of ADC with its additional input receiving, simultaneously, an additional signal isolated from the said analysed signal with the help of fundamental frequency isolation unit. The ADC sampling interval is selected to be constant to obtain simultaneously sequences of discrete samples of tested and additional signals. Then, proceeding from the additional signal discrete sampling sequence, the tested signal fundamental frequency cycle is computed along with the number of sampling intervals that more closely corresponds to fundamental frequency cycle value. Then, discrete samples with interval equal to the number of tested signal sampling intervals are selected from the sequence of tested signal discrete samples. Now, the correction factor equal to the ratio of product of the number of tested signal intervals by sampling interval to tested signal fundamental frequency cycle is calculated. Discrete harmonic analysis is made by multiplying arguments of all trigonometrical functions incorporated with the formulae for calculation of cosine and sine factors of Fourier series by aforesaid correction factor. The invention covers also the device for implementation of abode described method.

EFFECT: higher accuracy, possibility to calculate spectral components for every signal cycle.

2 cl, 4 dwg, 2 tbl

Description

The invention relates to measuring technique and can be used for discrete harmonic analysis of polyharmonic signals, including those characterized by rapid oscillations of the fundamental frequency, for example, when measuring the parameters of electrical networks with a rapidly changing load, the study of vibro-acoustic processes in electromechanical units, etc.

The classical technique for digital spectral analysis of signals is known from the prior art ([1] - Max J. Methods and techniques for processing signals in physical measurements. In 2 volumes, M., Mir, 1983, vol. 2, pp. 84-94) which consists in sampling the signal by analog-to-digital conversion and multiplying the sequence of discrete samples by a time window to obtain a sample of discrete samples. To reduce the influence of the finiteness of the sample on the accuracy of the spectral analysis, the so-called "window effect", the sample is multiplied by a smoothly changing function that vanishes outside the window (weight function). Further, the calculation of the spectral components of the signal spectrum is carried out by the discrete Fourier transform method.

It is also known a device ([1], t.2, p. 87, Fig. 19.8) for implementing this method, comprising a low-pass filter, an analog-to-digital converter, a memory unit, an arithmetic device and an averager. The input of the low-pass filter is intended for the input of the signal under study, and the output is connected to the input of an analog-to-digital converter, the output of which is connected to the input of the memory unit. An arithmetic device is associated with the memory. The output of the memory block is connected to the input of the averager, the output of which is the information output of the device.

The disadvantage of the data of the method and device is that the accuracy of the calculation of the spectral components of the polyharmonic signal directly depends on how many periods of the studied signal fell into the time window and the sample of discrete samples. If the investigated physical process is stationary and the studied signals have a correspondingly constant frequency of the main (first) harmonic, then it is enough to choose the width of the time window depending on the required accuracy of the spectrum calculation ([1], t.2, p.90, Fig.19.9) and multiply the sample of discrete samples by the corresponding weight function to correct the "window effect". But if the frequency of the fundamental harmonic of the signal changes rapidly according to an unknown law (oscillates), then the accuracy of the calculation of the spectral components of the signal under study decreases sharply. Also, with this method, it is impossible to calculate the spectral components for each signal period, since several periods are taken for analysis at once, but the calculation result is one for all signal periods. In addition, the measurement information already obtained is additionally averaged over several measurement cycles, which makes it impossible to obtain reliable spectra for polyharmonic signals with fast oscillations of the fundamental frequency.

Also known is a method of digital spectral analysis ([2] - NPP ENERGOTECHNIKA. Electric energy quality meters "PECУPC-UF2", Operation Manual, 2005, p.4.5, [on-line] [found on 12/18/2007] http: //www.entp.ru/documentation/uf2_re.pdf), adopted as a prototype, in which the frequency of the main (first) harmonic of the signal is preliminarily measured to account for changes in the frequency of the signal. Then, the sampling frequency of the analog-to-digital Converter is adjusted in such a way as to obtain a certain number of discrete samples for the period of the measured value of the fundamental frequency of the signal. Then, discrete samples of the signal are obtained by analog-to-digital conversion and discrete harmonic analysis is performed using the discrete Fourier transform.

Also known is a device ([2], items 4.1-4.11, Fig. A1) for implementing this method, comprising a primary measuring transducer, an analog-to-digital converter and a computing device. The measured physical quantity is fed to the input of the primary measuring transducer. From its output, the signal under investigation is fed to the input of an analog-to-digital converter, from the output of which the measuring information is fed to the input of a computing device, the output of which is designed to provide spectral components of the signal under study.

The disadvantage of the data of the method and device is the decrease in the accuracy of the calculation of the spectrum in the case when the oscillation of the fundamental frequency of the measured signal occurs during the acquisition of discrete samples. This is due to the fact that the analog-to-digital converter is already tuned to the value of the period of the main frequency of the signal, which took place before the occurrence of frequency fluctuations, and the resulting change in frequency cannot be taken into account. As a result, there is a mismatch in the analysis time interval of the signal and the actual period of its fundamental frequency. In addition, during the operation of the prototype device, it is impossible to provide the possibility of calculating the spectrum of each signal period, which may be required, for example, when studying transient and starting modes of operation of various equipment. This is due to the fact that in this method and device, after preliminary measurement of the instantaneous frequency of the fundamental harmonic of the signal, a certain time is required to fine-tune the sampling frequency of the analog-to-digital converter, and during this time information about individual signal sections is inevitably lost.

The objective of the invention is to increase the accuracy of determining the spectral components of polyharmonic signals with rapid fluctuations of the fundamental frequency, while ensuring the possibility of calculating the spectral components for each signal period.

This problem is solved due to the fact that in the method of spectral analysis of a polyharmonic signal, which consists in obtaining a sequence of discrete samples of the studied signal by analog-to-digital conversion and conducting discrete harmonic analysis of the studied signal using the discrete Fourier transform, the main harmonic is extracted from the studied signal, form from it an additional signal, the sampling interval of the analog-to-digital conversion is set constant and receive the reliability of the discrete samples of the additional signal by analog-to-digital conversion simultaneously with the signal under investigation, then, on the basis of the obtained sequence of discrete samples of the additional signal, the frequency period of the fundamental harmonic of the signal under study is calculated, based on which the number of sampling intervals of the signal under investigation is determined, which is most consistent with the value of the period of the fundamental frequency investigated signal, then from a sequence of discrete samples of the signal, a sampling of discrete samples with a length equal to the number of sampling intervals of the studied signal is made, then the correction coefficient is calculated by the formula:

R = (NΔt) / T,

where R is a correction factor;

N is the number of sampling intervals of the investigated signal;

Δt is the sampling interval of the analog-to-digital conversion, s;

T is the period of the fundamental frequency of the investigated signal, s,

and discrete harmonic analysis is carried out on the obtained sample of discrete samples of the signal under investigation, while the arguments of all trigonometric functions included in the formulas for calculating the cosine and sine coefficients of the Fourier series are multiplied by a correction factor, and in the device for implementing this method containing a primary measuring transducer with an input for receiving a measured physical quantity and an output for issuing a test signal, an analog-to-digital converter, the input of which is connected connected to the output of the primary measuring transducer, and the computing device, the input of which is communicated with the output of the analog-to-digital converter, and the output is intended for issuing the spectral components of the signal under investigation, a block for extracting the main harmonic of the studied signal with an input connected to the output of the primary measuring transducer and an output and the analog-to-digital converter is made with an additional input connected to the output of the main harmonic extraction unit of the signal under study.

It is known that when conducting spectral analysis, inevitably there are errors in determining the spectrum, which is a reflection of the general physical principle, according to which "it is impossible to simultaneously determine the frequency and time" ([1], v.2, p. 87). In the digital spectral analysis of polyharmonic signals, the frequency of which fluctuates rapidly, additional errors arise due to the inability to take into account this change in frequency, because frequency fluctuations are generally random. The essence of the claimed invention is to compensate for the influence of frequency fluctuations on the accuracy of the calculation by determining the fundamental frequency of the signal while receiving its discrete samples. This, firstly, allows to increase the accuracy of the calculation of the spectral components of the signals regardless of the fundamental harmonic frequency fluctuations due to the subsequent correction of the calculation based on the measurement data of the instantaneous frequency of the signal that it had during sampling, and secondly, to provide the possibility of calculation spectrum of each signal period, since it becomes possible to choose a signal analysis time interval equal to the actual period of its fundamental frequency and it is not necessary to average the measurement results .

The invention is illustrated by drawings.

Figure 1 shows a functional diagram of a device for implementing the method of spectral analysis of a polyharmonic signal;

figure 2 - plot of instantaneous values of the investigated and additional signals;

figure 3 - diagram of the calculation of the period of the frequency of the fundamental harmonic of the investigated signal;

figure 4 is a spectrum of signal amplitudes for an example of calculation.

A device for implementing the method of spectral analysis of polyharmonic signals contains a primary measuring transducer 1, a unit 2 for extracting the fundamental harmonic of the signal under study, an analog-to-digital converter 3 and a computing device 4. The input of the primary measuring transducer 1 is intended for receipt of a measured physical quantity, and its output is intended for output the studied signal and is communicated with the input of the analog-to-digital converter 3 and with the input of block 2. The output of block 2 is communicated with an additional the input of the analog-to-digital Converter 3, the output of which is communicated with the input of the computing device 4, the output of which is designed to issue spectral components of the signal under study.

The method of spectral analysis of polyharmonic signals is as follows.

The measured physical quantity Ψ (t), which is a function of time t, is fed to the input of the primary measuring transducer 1, which performs all operations to convert the physical quantity Ψ (t) into the signal x (t) under study. From the output of the primary measuring transducer 1, the studied signal x (t) is fed to the input of the analog-to-digital converter 3 and in parallel to the input of block 2, which extracts the main harmonic from the studied signal x (t) and forms an additional signal s ( t). Next, an additional signal s (t) is supplied to the additional input of the analog-to-digital converter 3, where it is sampled simultaneously with the signal x (t) under study. The sampling interval of the analog-to-digital Converter 3 is set constant regardless of the fundamental frequency of the investigated signal x (t).

As a result of sampling, the output of the analog-to-digital converter 3 produces a single digital data stream containing two time-coordinated discrete sequences: a discrete sequence h [t] of the signal under investigation and a discrete sequence d [t] of the additional signal. The term "time-aligned" means that, firstly, frequency period T of the fundamental harmonic of the signal and the period T _ext fundamental frequency auxiliary signal are equal and, secondly, a discrete sequence of the additional signal is shifted relative to a discrete sequence of the signal at time τ necessary for processing the signal x (t) under study in block 2. The time τ is constant and is accurately taken into account in further calculations.

Next, the discrete sequence h [t] of the signal under investigation and the discrete sequence d [t] of the additional signal are fed to the input of computing device 4, where the period T _add and the number N of sampling intervals of the signal under investigation are determined, which corresponds most to the value of period T. For this, based on the obtained discrete the sequence d [t] of the additional signal determines the moments of transition of the additional signal s (t) through a zero value in the same direction. These time points in Fig. 2 are indicated by points A and B. The value of the discrete count in the discrete sequence d [t] for these moments should become equal to zero or change its sign in the same way: from plus to minus, or vice versa. The procedure for determining the time moments A and B is explained in detail in the diagram in Fig. 3, which shows the time axis t and the numerical axis m combined with it, and also marks the time moments A and B. The ordinate axis shows the values of discrete samples of the discrete sequence d [t ] additional signal. Since the sampling of signals and discrete harmonic analysis requires a transition from time t to its discrete values, and vice versa, then through the individual values m: m ₁ , m ₂ , m ₃ , m ₄ in Fig. 3, are simultaneously designated as moments of physical time, and serial numbers of discrete samples in a discrete sequence d [t] of an additional signal that correspond to these moments and for which discrete samples d [m ₁ ], d [m ₂ ], d [m ₃ ], d [m ₄ ] were obtained .

The interval between adjacent points in time, for example between time moments m ₁ and m ₂ , is the sampling interval Δt of the analog-to-digital conversion. Then, to determine the value of time t to which one or another value of m corresponds, it suffices to multiply the number of sampling intervals Δt by the difference between this value m and the value m corresponding to the first discrete sample in the sample of discrete samples, which will be performed later.

Since the additional signal s (t) contains only the fundamental harmonic and has a smooth shape without outliers and interference, the signal sections between the discrete samples d [m ₁ ] and d [m ₂ ] and between the discrete samples d [m ₃ ] and d [m ₄ ] can be represented by piecewise linear interpolation. The time moment m ₁ is the time moment at which a discrete sample d [m ₁ ] with serial number m ₁ was obtained and which precedes the intersection of the time axis t with a line interpolating the additional signal s (t) at point A. The next discrete sample d [ m ₂ ] obtained at time m ₂ after crossing the time axis t with a line interpolating the additional signal s (t) at point A. Time moment m ₃ is the time moment that precedes the intersection of the time axis with a line interpolating the additional signal s (t) at point B, and at which it was obtained discrete th countdown

d [m ₃ ] with serial number m ₃ . The next discrete sample d [m ₄ ] was obtained at time m ₄ after crossing the time axis t with signal s (t) at point B.

Figure 3 shows two lines necessary to determine the period T _add : the line between the discrete samples d [m ₁ ] and d [m ₂ ] intersects the time axis t at point A, and the line between the discrete samples d [m ₃ ] and d [m ₄ ] crosses the time axis t at point B. The period T _extra frequencies of the fundamental of the additional signal is determined by the formula:

T _add = t ₁ + t ₂ + t ₃ ,

where t ₁ - part of the sampling interval Δt between time A and time m ₂ , s;

t ₂ - part of the sampling interval Δt between time moment m ₃ and time point B, s;

t ₃ is the sum of whole sampling intervals Δt between time instants m ₂ and m ₃ , s.

Moreover, part t _{1 of} the sampling interval Δt is found from the similarity condition of triangles formed by the intersection of the time axis t, the line interpolating the additional signal s (t) and passing through point A, and the vertical lines passing through time instants m ₁ and m ₂ , and determined by the formula:

t ₁ = Δt (| d [m ₂ ] | / (| d [m ₂ ] | + | d [m ₁ ] |)),

where Δt is the sampling interval of the analog-to-digital conversion, s;

| d [m ₁ ] | - module discrete readings obtained at time m ₁ ;

| d [m ₂ ] | - module discrete readings obtained at time m ₂ .

Part t _{2 of} the sampling interval Δt is found from the similarity condition of triangles formed by the intersection of the time axis t, a line interpolating an additional signal s (t) and passing through point B, and vertical lines passing through time instants m ₃ and m ₄ , and is determined by the formula:

t ₂ = Δt (| d [m ₃ ] | / (| d [m ₄ ] | + | d [m ₃ ] |)),

where Δt is the sampling interval of the analog-to-digital conversion, s;

| d [m ₃ ] | - module discrete readings obtained at time m ₃ ;

| d [m ₄ ] | - module discrete readings obtained at time m ₄ .

The sum of the whole intervals t ₃ is determined by the formula:

t ₃ = Δt (m ₃ -m ₂ ),

where Δt is the sampling interval of the analog-to-digital conversion, s;

m ₂ is the number of a discrete count in a discrete sequence d [t] of an additional signal received at time m ₂ ;

m ₃ is the number of the discrete count in the discrete sequence d [t] of the additional signal received at time moment m ₃ .

Next, determine the number N of sampling intervals of the investigated signal, the most appropriate value of the period T, according to the formula:

N = (T / Δt),

where T is the period of the fundamental frequency of the investigated signal, s;

Δt is the sampling interval of the analog-to-digital conversion, s.

For further use, the resulting number N is rounded off by standard arithmetic rounding. The product of the number N by the sampling interval Δt is the analysis time interval of the studied signal, and due to the rounding procedure, the maximum discrepancy between the signal analysis time interval and the period of its fundamental frequency cannot exceed half the sampling interval Δt. In this case, the number N is arbitrary, which requires the use of the fast Fourier transform algorithm, since for the implementation of this algorithm the number of sampling intervals should be a power of 2. Since neither the fast Fourier transform algorithm nor other known fast transform algorithms affect the accuracy of calculations , and they allow one to only reduce the amount of computation, then due to the rejection of restrictions on the choice of values of the number N, a more complete coincidence of the signal analysis time interval is achieved a and its actual period of the fundamental frequency. In this case, the task of reducing the amount of computation is not relevant for the claimed invention.

After determining the number N from the discrete sequence h [t] of the investigated signal, discrete samples are sampled. To do this, first determine the number N _{A of the} discrete sample in the discrete sequence d [t] of the additional signal, corresponding to the time on the numerical axis m closest to the time A. Then, the delay of the additional signal s (t) relative to the original signal x ( t) for the time τ. Since time τ is a constant value, the discrete sequence d [t] of the additional signal is also delayed relative to the discrete sequence h [t] of the signal under study by the number N _{τ of} discrete samples, which is constant and is determined by the formula:

N _τ = τ / Δt,

where N _τ is the number of discrete samples by which the discrete sequence d [t] of the additional signal is delayed relative to the discrete sequence h [t] of the signal under study;

τ is the time required to process the studied signal x (t) in block 2, s;

Δt is the sampling interval of the analog-to-digital conversion, s.

For further use, the resulting number N _{τ is} also rounded off by standard arithmetic rounding. Then determine the number N _{0 of the} discrete count in the discrete sequence h [t] of the investigated signal, corresponding to the beginning of the period T, by the formula:

N ₀ = N _A -N _τ ,

where N _A is the number of the discrete count in the discrete sequence d [t] of the additional signal corresponding to the time on the numerical axis m closest to the time A;

N _τ is the number of discrete samples by which the discrete sequence d [t] of the additional signal is delayed relative to the discrete sequence h [t] of the signal under study.

A sample of discrete samples for discrete harmonic analysis is made from a discrete sequence h [t] of the signal under investigation starting from a sample with the number N ₀ and a length equal to the number N.

Next, a discrete harmonic analysis is carried out, for which the resulting sample of discrete samples is processed in accordance with the classical Fourier transform formulas without using fast transformation algorithms. It is known that when calculating the cosine and sine coefficients of the Fourier series for signals represented by discrete samples, the integrals included in the Fourier transform formulas are calculated by the rectangle method, i.e. the sum of the areas of the signal between adjacent discrete samples is calculated. Due to the frequency fluctuation of the signal under study, a difference arises between each adjacent area calculated for a given actual sampling interval and that area that should have been obtained with the exact coincidence of the analysis time interval with the signal frequency period T. As shown above, due to the fact that in this method of spectral analysis the number N of sampling intervals is determined by the most appropriate value of the frequency period of the fundamental harmonic of the signal under study, this discrepancy cannot exceed half the sampling interval Δt. To further compensate for this mismatch, the method claimed in the invention introduces a correction factor R, calculated by the formula:

R = (NΔt) / T,

where N is the number of sampling intervals of the investigated signal;

Δt is the sampling interval of the analog-to-digital conversion, s;

T is the period of the fundamental frequency of the investigated signal, s.

Further, in the process of conducting the discrete Fourier transform, the arguments of all trigonometric functions included in the formulas for calculating the cosine and sine coefficients of the Fourier series are multiplied by this correction coefficient R:

,

,

,

,

where k is the number of harmonics;

And _k is the cosine coefficient of the Fourier series for the k-th harmonic;

B _k is the sine coefficient of the Fourier series for the k-th harmonic;

N is the number of sampling intervals of the investigated signal;

N ₀ is the number of the discrete reference in the discrete sequence h [t] of the signal under investigation, corresponding to the beginning of period T;

[i + N ₀ ] is the current serial number of the sample in the discrete sample h [t] of the signal under study during summation;

h [i + N ₀ ] - discrete sample of the studied signal for the time [i + N ₀ ];

R is the correction factor.

The spectral components are found by the formulas:

,

,

φ _k = arctan (A _k / B _k ),

where M _k is the amplitude of the k-th harmonic;

φ _k is the phase angle of the kth harmonic.

The proposed method for the spectral analysis of polyharmonic signals and a device for its implementation also provide the ability to calculate the spectrum of each period of the signal under study without gaps in the sections of the signal under study due to the fact that the discrete sequence of the signal under investigation is fed to the input of computing device 4 continuously and simultaneously to the input of computing device 4 information necessary to determine the period of the fundamental frequency of the investigated signal. Moreover, no additional time is required to determine this period and, as a result, there are no gaps in the sections of the studied signal.

As an example of the implementation of the claimed invention, the calculation of the spectral components of the polyharmonic signal is provided, provided that the frequency oscillation of the fundamental harmonic of the signal occurs. For this, the calculation was made for two adjacent periods of the signal with different frequencies of the main harmonic of the signal. Other conditions: the spectral composition of the signal and the parameters of the analog-to-digital conversion are the same for both periods of the signal, which is necessary to ensure comparability of the results of calculations made for two periods of the signal. The fundamental frequency of the first period of the measured physical quantity Ψ (t) is 50.08 Hz. The fundamental frequency of the second period of the measured physical quantity Ψ (t) is 49.93 Hz, which is equivalent to a rapid decrease in the fundamental frequency of the process (occurrence of frequency fluctuations) by 0.15 Hz. At the output of the primary transducer 1, after converting the measured physical quantity Ψ (t), a polyharmonic signal x (t) was obtained. The amplitudes of harmonics are given in relative units (rel. Units). The signal x (t) is described, for example, by the following function of time:

,

,

where x (t) is the signal under investigation;

t is the time, s;

k is the number of harmonics;

M _k is the amplitude of the k-th harmonic, rel. units;

f ₁ - frequency of the main (first) harmonic, Hz;

φ _k is the phase angle of the kth harmonic, degree.

The amplitudes and phase angles of the harmonics are given in table 1. The amplitude of the fundamental harmonic is 100 rel. units: this allows you to get the results of calculating the amplitude spectrum, numerically equal to percent.

Table 1 TO one 2 3 four 5 6 7 8 9 10 M _k , rel. units one hundred 5 5 5 5 5 5 5 5 5 φ _k , deg. 0 -thirty +30 -thirty +30 -thirty +30 -thirty +30 -thirty

At the output of block 2, the main harmonic of the signal under study is selected and an additional signal s (t) is formed, containing only the main harmonic of the signal under study x (t). The signal s (t) is described by the following function of time:

s (t) = M _s sin (2πf ₁ (t-τ) + (φ ₁ ),

where s (t) is an additional signal;

M _s - the amplitude of the additional signal, rel. units;

f ₁ - frequency of the main (first) harmonic, Hz;

t is the time, s;

τ is the time required to process the studied signal x (t) in block 2, s;

φ ₁ - phase angle of the fundamental harmonic, degrees.

The amplitude of the additional signal M _s is 100. The dynamic range of the analog-to-digital conversion is from -110 to +110 rel. units The sampling interval Δt of the analog-to-digital conversion is 3.9 · 10 ^-5 s. The time τ is 0.001 s. The sequence of discrete samples h [t] for the studied signal x (t) and the sequence of discrete samples d [t] for the additional signal s (t) in the example were obtained by calculation. For this, the exact analytical values of the functions x (t) and s (t) were calculated for the time instants t separated by Δt. The obtained exact values of the functions x (t) and s (t) are converted to integers in accordance with the order of operation of the analog-to-digital converter, for which each value of the functions x (t) and s (t) is divided by the value of the dynamic range equal to 110, multiply by 2 ¹⁵ and round off with standard arithmetic rounding. The accuracy of such a conversion of the values of the functions x (t) and s (t) to integers corresponds to the accuracy of a 16-bit analog-to-digital conversion.

The magnitude of the period T of the frequency of the fundamental harmonic for the first period of the signal is determined in accordance with the above calculation method according to the scheme in figure 3 and is equal to 0.019968 s. The magnitude of the period T of the frequency of the fundamental harmonic for the second period of the signal is determined in a similar way and is equal to 0.020028 s. With these signal parameters, the number N of sampling intervals is 512 for the first signal period and the number N is 514 for the second signal period. The analysis time interval for the first signal period includes 512 sampling intervals and is equal to 0.019968 s. The analysis time interval for the second signal period includes 514 sampling intervals and is equal to 0.020046 s. The difference between the analysis time interval for the second signal period and the period of its main frequency is 1.8 · 10 ^-5 s, which is 46.154% of Δt and is close to the maximum possible value of the signal analysis time interval for the proposed method of spectral analysis for its period fundamental frequency. The correction factor for the first signal period is R = (512 · 3.9 · 10 ^-5 ) /0.019968 = 1.0. The correction factor for the second signal period is R = (514 · 3.9 · 10 ^-5 ) / 0.020028 = 1.000899.

Then, the spectral components M _k and φ _{k are} calculated by the method of the discrete Fourier transform, during which the arguments of all the trigonometric functions included in the formulas for calculating the cosine coefficients A _k and the sine coefficients B _k of the Fourier series are multiplied by the correction coefficient R.

The calculation results of the spectral components of the signal x (t) are shown in table 2.

table 2 Garmo
nick k The fundamental frequency of the signal f ₁ Hz Spectral component The amplitude value of M _k , rel. units Phase angle φ _k , degree Prototype The claimed method Prototype The claimed method 2 50.08 5,0002 5,0000 -30.00 -30.00 49.93 5,2507 5,0032 -28.14 -30.07 3 50.08 5,0001 5,0000 +30.00 +30.00 49.93 5,1306 4,9968 +29.62 +29.93 four 50.08 5,0000 5,0000 -30.00 -30.00 49.93 5,0400 5,0032 -29.42 -30.07 5 50.08 5,0001 5,0000 +30.00 +30.00 49.93 5.0594 4,9968 30, 06 +29.93 6 50.08 4,9999 4,9999 -30.00 -30.00 49.93 5,0190 5,0034 -29.57 -30.07 7 50.08 5,0000 5,0000 +30.00 +30.00 49.93 5.0780 4,9968 +29.93 +29.93 8 50.08 5,0001 5,0000 -30.00 -30.00 49.93 5.0677 5,0034 -29.23 -30.07 9 50.08 5,0001 5,0000 +30.00 +30.00 49.93 5.1838 4,9969 +29.37 +29.93 10 50.08 5,0002 5,0000 -30.00 -30.00 49.93 5.2524 5,0035 -27.66 -30.07

Table 2 also shows the results obtained when calculating the spectrum of the signal x (t) according to the prototype with the same initial data as in the present method. According to the prototype, the number N of sampling intervals for calculation for the first and second signal periods is the same and equal to 512, and the sampling interval Δt of the analog-to-digital conversion for the second signal period is determined so that 512 measurements of instantaneous values are made for the previous (first) period of the fundamental frequency the investigated signal. For the value of the fundamental frequency of the first period equal to 50.08 Hz, the sampling interval Δt is 3.9 · 10 ^-5 s, as well as for the method claimed in the invention, which allows one to correctly compare the calculation results of the prototype and the claimed method. Figure 4 shows the amplitude spectrum M _k obtained by this method for the second period of the signal with a fundamental frequency of 49.93 Hz.

As can be seen from table 2, the maximum absolute error in determining the amplitude of the harmonics of the signal x (t) is 0.035, which is 0.07%, and the error in determining the phase angle is 0.07 degrees. For the prototype, the maximum absolute error in determining the harmonic amplitude of the signal x (t) is 0.2524, which is 5.048%, and the error in determining the phase angle is 5.75 degrees. This indicates that the claimed method and device for its implementation can improve the accuracy of the determination of the spectral components of polyharmonic signals with rapid fluctuations of the fundamental frequency. In addition, as can be seen from the amplitude spectrum in figure 4, obtained by the method claimed in the invention, this spectrum practically does not contain harmonics that were not in the studied signal x (t), which indicates the absence of manifestation of known effects (Gibbs effect, etc. .) caused by the influence of the finiteness of the sample and reducing the accuracy of the spectral analysis.

Moreover, it can be seen from the implementation example that all the information necessary and sufficient for the exact calculation of the spectral components of the polyharmonic signal is obtained simultaneously with the analog-to-digital conversion for a time equal to the magnitude of the frequency period of the fundamental signal harmonic. This makes it possible to calculate the spectral components for each signal period.

Claims (2)

1. The method of spectral analysis of polyharmonic signals, which consists in obtaining a sequence of discrete samples of the signal under investigation by analog-to-digital conversion and performing discrete harmonic analysis of the signal under investigation using the discrete Fourier transform, characterized in that its main harmonic is extracted from the signal under investigation, and an additional harmonic is formed from it the signal, the sampling interval of the analog-to-digital conversion is set constant and a sequence of discrete counts of the additional signal by analog-to-digital conversion simultaneously with the signal under investigation, then, based on the obtained sequence of discrete samples of the additional signal, the frequency period of the fundamental harmonic of the signal under investigation is calculated, based on which the number of sampling intervals of the signal under investigation is determined, which is most consistent with the value of the frequency period of the fundamental harmonic of the signal under investigation , then from a sequence of discrete samples of the investigated signal produce a sample of discrete samples with a length equal to the number of sampling intervals of the studied signal, then the correction coefficient is calculated by the formula:
R = (NΔt) / T,
where R is a correction factor;
N is the number of sampling intervals of the investigated signal;
Δt is the sampling interval of the analog-to-digital conversion, s;
T is the period of the fundamental frequency of the investigated signal, s,
and discrete harmonic analysis is carried out on the obtained sample of discrete samples of the signal under study, while the arguments of all trigonometric functions included in the formulas for calculating the cosine and sine coefficients of the Fourier series are multiplied by a correction coefficient. 2. The device for implementing the method according to claim 1, containing a primary measuring transducer with an input for receiving a measured physical quantity and an output for issuing a test signal, an analog-to-digital converter, the input of which is connected to the output of the primary measuring transducer, and a computing device whose input is communicated with the output of an analog-to-digital converter, and the output is intended for the issuance of the spectral components of the signal under study, characterized in that the main ha isolation unit is introduced the harmonics of the signal under study with an input connected to the output of the primary measuring transducer and the output, and the analog-to-digital converter is made with an additional input connected to the output of the main harmonic extraction unit of the signal being studied.

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