CN111579868B - Method and device for measuring higher harmonics - Google Patents

Method and device for measuring higher harmonics Download PDF

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CN111579868B
CN111579868B CN202010447865.8A CN202010447865A CN111579868B CN 111579868 B CN111579868 B CN 111579868B CN 202010447865 A CN202010447865 A CN 202010447865A CN 111579868 B CN111579868 B CN 111579868B
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CN111579868A (en
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郭成
段锐敏
曾野
覃日升
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Electric Power Research Institute of Yunnan Power Grid Co Ltd
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Electric Power Research Institute of Yunnan Power Grid Co Ltd
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Abstract

The application provides a method and a device for measuring higher harmonics. The method comprises the following steps: after a window function is added to a sampled time domain of the higher harmonic signal to be measured and fast discrete Fourier transform is carried out, convolution operation is carried out on the sampled time domain of the higher harmonic signal to be measured and continuous Fourier transform of the same window function, a maximum signal point with a maximum convolution operation result value is determined, the frequency of the maximum signal point is determined as the frequency of the higher harmonic signal to be measured, and the amplitude of the higher harmonic signal to be measured and the phase of the higher harmonic signal to be measured are determined according to the frequency of the higher harmonic signal to be measured and the conversion relation between preset frequency, amplitude and phase. Therefore, the phase delay after time domain windowing is offset at the frequency point of the higher harmonic signal to be measured, the convolution reaches an extreme value, the transcendental equation does not need to be solved in the whole calculation process, polynomial fitting is not involved, only algebraic operation is needed, the calculation amount is small, the calculation difficulty is not high, and the practical value is high.

Description

Method and device for measuring higher harmonics
Technical Field
The present disclosure relates to the field of power quality technologies, and in particular, to a method and an apparatus for measuring higher harmonics.
Background
With the wide application of various nonlinear load devices in power systems, the problem of higher harmonic pollution is increasingly aggravated. The higher harmonics can shorten the service life of related equipment in an electric power system, increase the energy consumption of an electric power circuit, simultaneously interfere nearby communication equipment and circuits, and seriously affect the quality of electric energy, so that the method has important significance in accurately detecting and analyzing the higher harmonics.
At present, frequency spectrum leakage usually occurs in the measurement process of higher harmonics. In order to reduce the influence of frequency spectrum leakage on the measurement accuracy of higher harmonics, the prior art generally adopts a time domain windowing function method to reduce the frequency spectrum leakage, and on the basis, a spectrum interpolation method is adopted to measure the higher harmonics, however, the spectrum interpolation method generally adopts polynomial interpolation fitting, the calculated amount is increased along with the increase of spectral lines required by calculation, and meanwhile, the method also relates to solving an transcendental equation, and the calculation difficulty is high.
Based on this, there is a need for a method for measuring higher harmonics, which is used to solve the problems of the prior art that the calculation amount for measuring higher harmonics is large and the calculation difficulty is high.
Disclosure of Invention
The application provides a method and a device for measuring higher harmonics, which can be used for solving the technical problems of large calculation amount and high calculation difficulty in measuring the higher harmonics in the prior art.
In a first aspect, an embodiment of the present application provides a method for measuring a higher harmonic, where the method includes:
acquiring a higher harmonic signal to be measured;
sampling the high-order harmonic signal to be measured according to a preset frequency to obtain a plurality of sampled signal points;
processing the plurality of signal points by adopting a preset window function respectively to obtain a plurality of processed signal points;
respectively carrying out fast discrete Fourier transform on the plurality of processed signal points to obtain a plurality of signal points after fast discrete Fourier transform;
performing continuous Fourier transform on the preset window function, and performing convolution operation on the window function after the continuous Fourier transform and the signal points after the multiple fast discrete Fourier transforms to obtain multiple signal points after the convolution operation;
determining a maximum signal point with the maximum convolution operation result value from the signal points after the convolution operation, and determining the frequency of the maximum signal point as the frequency of the high-order harmonic signal to be measured;
and determining the amplitude of the to-be-measured high-order harmonic signal and the phase of the to-be-measured high-order harmonic signal according to the frequency of the to-be-measured high-order harmonic signal and the conversion relation between the preset frequency and the amplitude and the phase.
In an implementation manner of the first aspect, the plurality of sampled signal points is represented by the following formula:
Figure BDA0002506594350000011
wherein x (m Δ t) represents the sampled signal point, m is a natural number, Δ t is a discrete time interval, A is the amplitude of the higher harmonic signal to be measured, ω is0Is the frequency of the higher harmonic signal to be measured,
Figure BDA0002506594350000012
is the phase of the higher harmonic signal to be measured.
In an implementation manner of the first aspect, the width of the preset window function is:
T＝N×Δt
where T is the width of the preset window function, N is an even number, representing the number of signal points after processing, and Δ T is the discrete time interval.
In an implementation manner of the first aspect, the plurality of fft signal points are determined by the following formula:
Figure BDA0002506594350000021
wherein, XW (n ω)s) Representing the signal points after the fast discrete Fourier transform, N is an integer between (-N/2) +1 and N/2, Z is an integer, N is an even number and represents the number of the signal points after the processing, omegasIs the frequency domain resolution, A is the amplitude of the higher harmonic signal to be measured, omega0Is the frequency of the higher harmonic signal to be measured,
Figure BDA0002506594350000026
is the phase of the higher harmonic signal to be measured, T is the width of the predetermined window function, j is the unit of imaginary number, W (n ωs) Representing a window function after a fast discrete Fourier transform, W (n ω @)s-ω0) Is frequency-shifted by ω from the window function after the fast discrete Fourier transform0And (4) obtaining the product.
In an implementation manner of the first aspect, the plurality of signal points after convolution operation are determined by using the following formula:
Figure BDA0002506594350000022
XWW (omega) represents the signal point after the convolution operation, omega represents the frequency of any signal point after the convolution operation, H is a positive integer, 2H +1 spectral lines need to cover the main lobe after the fast discrete Fourier transform of the preset window function, and XW (n omega)s) Representing said signal points after said fast discrete Fourier transform, ωsIs the frequency domain resolution, T is the width of a preset window function, j is an imaginary unit, W (omega) represents the window function after continuous Fourier transform, W (omega-n omega)s) Is frequency-shifted by n omega to the right by the window function after the continuous Fourier transformsAnd (4) obtaining the product.
In an implementable manner of the first aspect, the amplitude of the higher harmonic to be measured is determined using the following formula:
Figure BDA0002506594350000023
where A is the amplitude of the higher harmonic to be measured, XWW (ω)0) Represents the maximum signal point, ω, at which the convolution result value is maximum0Is the frequency of the higher harmonic signal to be measured, H is a positive integer, 2H +1 spectral lines need to cover the main lobe after the fast discrete Fourier transform of the preset window function, omegasIs the frequency domain resolution, | | is the absolute value, W (n ω |)s) Representing a window function after a fast discrete Fourier transform, W (n ω @)s-ω0) Is derived from the fast discrete Fourier transformFrequency right shift omega of window function after conversion0Obtaining;
the phase of the higher harmonic to be measured is determined by the following formula:
Figure BDA0002506594350000024
wherein the content of the first and second substances,
Figure BDA0002506594350000025
is the phase of the higher harmonic to be measured, XWW (ω)0) Representing the maximum signal point at which the result of said convolution operation is maximum, arg being XWW (ω)0) The principal value of the phase angle of (c).
In an implementation manner of the first aspect, determining a maximum signal point with a maximum convolution operation result value from the plurality of signal points after convolution operation includes:
and determining the maximum signal point with the maximum convolution operation result value from the plurality of signal points after convolution operation by adopting a gradient rising method.
In an implementation manner of the first aspect, an operation initial value of the gradient ascent method is determined by:
generating a signal amplitude-frequency diagram according to the signal points after the plurality of fast discrete Fourier transforms;
determining a first signal point with the maximum amplitude, a second signal point adjacent to the left of the first signal point and a third signal point adjacent to the right of the first signal point from the signal amplitude-frequency diagram;
judging whether the amplitude of the second signal point is greater than or equal to the amplitude of the third signal point or not, and if the amplitude of the second signal point is greater than or equal to the amplitude of the third signal point, obtaining an operation initial value of the gradient rising method according to the frequency of the first signal point and the frequency of the second signal point;
and if the amplitude of the second signal point is smaller than that of the third signal point, obtaining an operation initial value of the gradient rising method according to the frequency of the first signal point and the frequency of the third signal point.
In a second aspect, an embodiment of the present application provides an apparatus for measuring higher harmonics, the apparatus including:
the acquisition unit is used for acquiring a to-be-measured higher harmonic signal;
the processing unit is used for sampling the higher harmonic signal to be measured according to a preset frequency to obtain a plurality of sampled signal points; processing the sampled signal points by adopting a preset window function to obtain a plurality of processed signal points; respectively carrying out fast discrete Fourier transform on the processed signal points to obtain a plurality of fast discrete Fourier transformed signal points; performing continuous Fourier transform on the preset window function, and performing convolution operation on the window function subjected to continuous Fourier transform and the signal points subjected to fast discrete Fourier transform to obtain a plurality of signal points subjected to convolution operation; determining a maximum signal point with the maximum convolution operation result value from the signal points after the convolution operation, and determining the frequency of the maximum signal point as the frequency of the high-order harmonic signal to be measured; and determining the amplitude of the high-order harmonic signal to be measured and the phase of the high-order harmonic signal to be measured according to the frequency of the high-order harmonic signal to be measured and the conversion relation between the preset frequency and the amplitude and the phase.
In an implementation manner of the second aspect, the plurality of sampled signal points are represented by the following formula:
Figure BDA0002506594350000031
wherein x (m Δ t) represents the sampled signal point, m is a natural number, Δ t is a discrete time interval, A is the amplitude of the higher harmonic signal to be measured, ω is0Is the frequency of the higher harmonic signal to be measured,
Figure BDA0002506594350000034
is the phase of the higher harmonic signal to be measured.
In an implementable manner of the second aspect, the width of the preset window function is:
T＝N×Δt
where T is the width of the preset window function, N is an even number, representing the number of signal points after processing, and Δ T is the discrete time interval.
In an implementable manner of the second aspect, the plurality of fft signal points is determined using the following equation:
Figure BDA0002506594350000032
wherein, XW (n ω)s) Representing the signal points after the fast discrete Fourier transform, N is an integer between (-N/2) +1 and N/2, Z is an integer, N is an even number and represents the number of the signal points after the processing, omegasIs the frequency domain resolution, A is the amplitude of the higher harmonic signal to be measured, omega0Is the frequency of the higher harmonic signal to be measured,
Figure BDA0002506594350000035
is the phase of the higher harmonic signal to be measured, T is the width of the predetermined window function, j is the unit of imaginary number, W (n ωs) Representing a window function after a fast discrete Fourier transform, W (n ω @)s-ω0) Is frequency-shifted by ω from the window function after the fast discrete Fourier transform0And (4) obtaining the product.
In one implementation manner of the second aspect, the plurality of convolution-operated signal points are determined by using the following formula:
Figure BDA0002506594350000033
XWW (omega) represents the signal point after the convolution operation, omega represents the frequency of any signal point after the convolution operation, H is a positive integer, 2H +1 spectral lines need to cover the main lobe after the fast discrete Fourier transform of the preset window function, and XW (n omega)s) Representing said signal points after said fast discrete Fourier transform, ωsIs the frequency domain resolution, T is the width of a preset window function, j is an imaginary unit, W (omega) represents the window function after continuous Fourier transform, W (omega-n omega)s) Is frequency-shifted by n omega to the right by the window function after the continuous Fourier transformsAnd (4) obtaining the product.
In an implementable manner of the second aspect, the amplitude of the higher harmonic to be measured is determined using the following formula:
Figure BDA0002506594350000041
where A is the amplitude of the higher harmonic to be measured, XWW (ω)0) Represents the maximum signal point, ω, at which the convolution result value is maximum0Is the frequency of the higher harmonic signal to be measured, H is a positive integer, 2H +1 spectral lines need to cover the main lobe after the fast discrete Fourier transform of the preset window function, omegasIs the frequency domain resolution, | | is the absolute value, W (n ω |)s) Representing a window function after a fast discrete Fourier transform, W (n ω @)s-ω0) Is frequency-shifted by ω from the window function after the fast discrete Fourier transform0Obtaining;
the phase of the higher harmonic to be measured is determined by the following formula:
Figure BDA0002506594350000042
wherein the content of the first and second substances,
Figure BDA0002506594350000043
is the phase of the higher harmonic to be measured, XWW (ω)0) Representing the maximum signal point at which the result of said convolution operation is maximum, arg being XWW (ω)0) The principal value of the phase angle of (c).
In an implementable manner of the second aspect, the processing unit is specifically configured to:
and determining the maximum signal point with the maximum convolution operation result value from the plurality of signal points after convolution operation by adopting a gradient rising method.
In an implementable manner of the second aspect, the processing unit is specifically configured to:
generating a signal amplitude-frequency diagram according to the signal points after the plurality of fast discrete Fourier transforms; determining a first signal point with the maximum amplitude, a second signal point adjacent to the left of the first signal point and a third signal point adjacent to the right of the first signal point from the signal amplitude-frequency diagram; judging whether the amplitude of the second signal point is larger than or equal to the amplitude of the third signal point or not, and if the amplitude of the second signal point is larger than or equal to the amplitude of the third signal point, obtaining an operation initial value of the gradient rising method according to the frequency of the first signal point and the frequency of the second signal point; and if the amplitude of the second signal point is smaller than the amplitude of the third signal point, obtaining an operation initial value of the gradient rising method according to the frequency of the first signal point and the frequency of the third signal point.
Therefore, after the sampled signal time domain windowing function is subjected to fast discrete Fourier transform, convolution calculation is carried out with the continuous Fourier transform of the same window function, phase delay after the time domain windowing is offset at the frequency point of the higher harmonic signal to be measured, and the convolution reaches an extreme value.
Drawings
Fig. 1 is a schematic flowchart of a harmonic measurement method according to an embodiment of the present disclosure;
fig. 2a is a schematic diagram of 10 cycles of the harmonic signals acquired in the embodiment of the present application;
fig. 2b is a schematic diagram of 1 cycle of the obtained higher harmonic signal in the embodiment of the present application;
FIG. 3a is a schematic amplitude-frequency diagram of a fundamental wave after fast discrete Fourier transform in an embodiment of the present application;
FIG. 3b is a schematic diagram of the amplitude and frequency of the main higher harmonic after fast discrete Fourier transform in the embodiment of the present application;
FIG. 4 is a diagram illustrating the convolution result of the main higher harmonic after fast discrete Fourier transform and the window function after continuous Fourier transform in the embodiment of the present application;
fig. 5 is a schematic flowchart illustrating an integrity of a harmonic measurement method according to an embodiment of the present disclosure;
fig. 6 is a schematic structural diagram of a device for measuring higher harmonics according to an embodiment of the present application.
Detailed Description
To make the objects, technical solutions and advantages of the present application more clear, embodiments of the present application will be described in further detail below with reference to the accompanying drawings.
With the wide application of various nonlinear load power electronic devices in power systems, the problem of higher harmonic pollution generated by the nonlinear load power electronic devices is increasingly aggravated. The higher harmonics bring much harm to the power system, so that the method has important significance in accurately detecting and analyzing the higher harmonics. The frequency spectrum leakage usually occurs in the measurement process of the higher harmonic wave, and the higher harmonic wave frequency and the switching frequency f emitted by the converter containing the fully-controlled power electronic devicesAnd fundamental frequency f1In connection with this, a typical higher harmonic frequency distribution is f ═ mfs±nf1M, N belongs to N. The Ed.2.1 version of the standard IEC 61000-4-7 stipulates that the higher harmonic waves in the range of 2 kHz-9 kHz take 10 cycles of power frequency under the synchronous condition and are added with a rectangular window for fast discrete Fourier transform, although the frequency resolution is enough, the carrier frequency of the power electronic converter is not necessarily exactly integral multiple of the fundamental frequency, so the measurement of the higher harmonic waves can generate frequency spectrum leakage. The IEC standard algorithm reduces the influence of frequency spectrum leakage on higher harmonic measurement by expanding frequency domain bandwidth, but the algorithm is not suitable for the problems of higher harmonic traceability, resonance fault diagnosis and the like, so that the IEC standard algorithm effectively reduces the frequency spectrum leakage and ensures the higher harmonic measurement accuracy, and is a problem which is urgently needed to be solved in engineering application.
In view of the above situation, in the prior art, a method of adding a suitable window function in a time domain and performing spectral interpolation in a frequency domain is generally adopted, and commonly used window functions include a rectangular window, a Hanning (Hanning) window, various combination windows and the like. However, the spectral interpolation method usually adopts polynomial interpolation fitting, a transcendental equation needs to be solved, the calculation difficulty is high, the polynomial order cannot be too high, otherwise the longge (Runge) phenomenon of polynomial interpolation occurs, the calculation precision is sacrificed, and the calculation amount is increased along with the increase of spectral lines required by calculation.
In order to solve the problem, an embodiment of the present application provides a method for measuring a higher harmonic, which is specifically used for solving the problems of a large calculation amount and a high calculation difficulty in a higher harmonic measurement process. Fig. 1 is a schematic flow chart corresponding to a harmonic measurement method according to an embodiment of the present application. The method specifically comprises the following steps:
step 101, acquiring a high-order harmonic signal to be measured.
And 102, sampling the high-order harmonic signal to be measured according to a preset frequency.
And 103, processing the sampled signal points by adopting a preset window function.
And 104, performing fast discrete Fourier transform on the processed signal points.
And 105, performing continuous Fourier transform on the preset window function, and performing convolution operation on the window function after the continuous Fourier transform and the signal points after the fast discrete Fourier transform.
And 106, determining the maximum signal point with the maximum convolution operation result value from the signal points after the convolution operation, and determining the frequency of the maximum signal point as the frequency of the high-order harmonic signal to be measured.
And 107, determining the amplitude of the high-order harmonic signal to be measured and the phase of the high-order harmonic signal to be measured according to the frequency of the high-order harmonic signal to be measured and the conversion relation between the preset frequency and the amplitude and the phase.
In the embodiment of the application, after time domain windowing is carried out on the high-order harmonic signals to be measured and fast discrete Fourier transform calculation frequency spectrum is carried out, convolution operation is carried out with continuous Fourier transform of the same window function, polynomial fitting is not involved in the whole solving process, only algebraic operation is contained, the operation amount is small, the operation complexity is low, and the practicability is high.
Specifically, in step 101, the harmonic is each order component having a frequency greater than an integral multiple of the fundamental frequency, that is, a sine component or a cosine component having a frequency that is an integral multiple of the fundamental frequency, which is obtained by fourier series decomposition of the periodic non-sinusoidal alternating current component. In the embodiment of the present application, the acquired higher harmonic signal is continuous in the time domain.
In step 102, a to-be-measured higher harmonic signal is sampled according to a preset frequency, that is, a signal with a continuous time domain is dispersed into signal points according to a preset time interval, and a plurality of signal points obtained after sampling are expressed by the following formula:
Figure BDA0002506594350000061
in formula (1), x (m Δ t) represents a sampled signal point, m is a natural number, Δ t is a discrete time interval, a is an amplitude of a higher harmonic signal to be measured, ω is0Is the frequency of the higher harmonic signal to be measured,
Figure BDA0002506594350000065
is the phase of the higher harmonic signal to be measured.
In step 103, a window function w (m Δ T) with a width T is used to process the signal point x (m Δ T), where the width of the window function is:
formula (2) of (N × Δ T)
In equation (2), T is the width of the preset window function, N is an even number, which represents the number of signal points after processing, and Δ T is the discrete time interval.
In the embodiment of the present application, there are many types of window functions, and the difference between the various window functions mainly lies in the ratio between the energy concentrated on the main lobe and the energy dispersed on all side lobes, and a suitable window function may be selected to effectively reduce the spectral leakage.
In step 104, performing fast discrete fourier transform on the windowed signal points, and determining the obtained fast discrete fourier transformed signal points by using the following formula:
Figure BDA0002506594350000062
in the formula (3), XW (n ω)s) Representing the signal points after the fast discrete Fourier transform, N is an integer between (-N/2) +1 and N/2, Z is an integer, N is an even number and represents the number of signal points after windowing, omegasIs the frequency domain resolution, A is the amplitude of the higher harmonic signal to be measured, omega0Is the frequency of the higher harmonic signal to be measured,
Figure BDA0002506594350000066
is the phase of the higher harmonic signal to be measured, T is the width of the predetermined window function, j is the unit of imaginary number, W (n ωs) Representing a window function after a fast discrete Fourier transform, W (n ω @)s-ω0) Is frequency-shifted to the right by ω from the window function after the fast discrete Fourier transform0And (4) obtaining the product.
In step 105, convolving the signal points after the fast discrete fourier transform with the window function after the continuous fourier transform, and determining the signal points after the convolution operation by adopting the following formula:
Figure BDA0002506594350000063
in the formula (4), XWW (ω) represents a signal point after convolution operation, ω is the frequency of any signal point after convolution operation, n is an integer with a value between-H and H, H is a positive integer, 2H +1 spectral lines need to cover a main lobe after fast discrete Fourier transform of a preset window function, and XW (n ω) is obtaineds) Representing signal points after a fast discrete Fourier transform, omegasIs the frequency domain resolution, T is the width of a preset window function, j is an imaginary unit, W (omega) represents the window function after continuous Fourier transform, W (omega-n omega)s) Is frequency-shifted by n omega to the right by the window function after the continuous Fourier transformsAnd (4) obtaining the product.
In step 106, there are various ways to determine the maximum signal point with the maximum convolution result value, and in one example, the maximum signal point with the maximum convolution result value may be determined by using a gradient ascent method. The method can be specifically realized by the following steps:
setting a loss function of a gradient ascent method:
j (ω) ═ XWW (ω) | formula (5)
In the formula (5), XWW (ω) represents the signal point after convolution operation, and J (ω) represents the loss function, which is obtained by taking the absolute value of XWW (ω), i.e., the modulus of XWW (ω).
Setting an updating formula:
Figure BDA0002506594350000064
ω (k +1) ═ ω (k) + Δ ω (k) equation (7)
In formula (6) and formula (7), k is the number of cycles, starting from 2; ω (k) is the kth ω taken in the cycle, Δ ω (k) represents the difference between the kth +1 ω and the kth ω in the cycle, i.e., the update degree of ω (k), J (ω (k)) represents the modulus of XWW (ω (k)), i.e., the modulus of the convolution operation result with frequency ω (k), and η ∈ (0,1) is the learning rate.
Setting operation initial values delta omega (1) and delta J (omega (1)) for a gradient rising method, circularly calculating a formula (6) and a formula (7) by k from 2 until the calculated | delta omega | is obtained, namely the absolute value of delta omega is smaller than a preset threshold delta, stopping circularly calculating, wherein a signal point corresponding to omega (k) when the circularly calculating is stopped is a maximum signal point with a maximum convolution operation result value, and taking omega (k) as the frequency omega (1) of a high-order harmonic signal to be measured0。
By adopting the convolution method, the frequency of the higher harmonic signal to be measured just falls on the point of the maximum value of the convolution result, and the gradient ascent method is adopted for circular calculation when the maximum value of the convolution result is solved, so that the calculation times of convolution can be reduced, polynomial fitting is not involved, only algebraic operation is performed in the whole process, the calculation difficulty is low, and the practical value is high.
In other possible examples, the person skilled in the art may determine the maximum signal point with the maximum convolution result value according to experience and practical situations, for example, the maximum signal point may be calculated by using a neural network, and the method is not limited in particular.
In one example, an amplitude-frequency map is generated from signal points obtained by performing fast discrete fourier transform after windowing a signal time domain, and a frequency corresponding to a signal point with the largest amplitude and a frequency corresponding to a signal point with a larger adjacent amplitude are searched from the amplitude-frequency map as the operation initial values of the gradient ascent method, which can be specifically realized by the following steps:
and generating a signal amplitude-frequency diagram according to the signal points after the fast discrete Fourier transform.
A first signal point with the maximum amplitude, a second signal point adjacent to the left of the first signal point and a third signal point adjacent to the right of the first signal point are determined from the signal amplitude-frequency diagram.
Judging whether the amplitude of the second signal point is larger than or equal to the amplitude of the third signal point, if so, judging the frequency omega of the first signal pointp1And the frequency omega of the second signal pointp2And obtaining an operation initial value of the gradient ascending method.
If the amplitude of the second signal point is smaller than the amplitude of the third signal point, the frequency ω according to the first signal pointp1And the frequency ω of the third signal pointp3And obtaining an operation initial value of the gradient ascending method.
It should be noted that, when the amplitude of the second signal point is equal to the amplitude of the third signal point, the frequency ω of the first signal point may also be usedp1And the frequency ω of the third signal pointp3Obtaining the initial value of the gradient ascent method。
Assuming that the determined initial frequency of operation is ωp1And omegap2Then, the operation initial value of the gradient ascent method is determined by the following formula:
ΔJ(ω(1))＝J(ωp1)-J(ωp2) Formula (8)
Δω(1)＝ωp1-ωp2Formula (9)
In the formula (8) and the formula (9), ωp1Is the frequency, ω, corresponding to the first signal point with the largest amplitudep2Is the frequency corresponding to the signal point with the larger amplitude in the two adjacent signal points at the left and right sides of the first signal point with the largest amplitude, wherein delta omega (1) represents the updating degree of the first omega in the updating formula (6) and the updating formula (7), and J (omega)p1) Representation XWW (ω)p1) Of (e), i.e. of frequency ωp1Modulo J (ω) of the result of the convolution operation of (c)p2) Representation XWW (ω)p2) Of the mode, i.e. with frequency ωp2The modulus of the convolution operation result of (2), Δ J (ω (1)), represents the frequency ωp1The modulus and the frequency of the convolution operation result of (2) are ωp2The difference of the modes of the result of the convolution operation.
By adopting the method in the example to set the operation initial value for the gradient ascending method, the calculation range of convolution can be reduced, the calculation amount is reduced, the calculation speed of solving the maximum value is improved, and the method is easy to realize quickly.
In other possible examples, a person skilled in the art may determine the operation initial value for the gradient ascent method according to experience and practical situations, for example, a frequency corresponding to a signal point with the largest amplitude in a signal amplitude frequency diagram after windowed fourier transform and a frequency corresponding to a signal point with the second largest amplitude may be used as the initial frequency for the gradient ascent method operation, or two frequencies may be randomly designated as the initial frequencies for the gradient ascent method operation, which is not limited in particular.
In step 107, the amplitude of the higher harmonic to be measured is determined by using the following formula:
Figure BDA0002506594350000081
in the formula (10), A is the amplitude of the higher harmonic to be measured, XWW (ω)0) Represents the maximum signal point, ω, at which the convolution result value is maximum0Is the frequency of the higher harmonic signal to be measured, H is a positive integer, 2H +1 spectral lines need to cover the main lobe after the fast discrete Fourier transform of the preset window function, omegasIs the frequency domain resolution, | | is the absolute value, W (n ω |)s) Representing a window function after a fast discrete Fourier transform, W (n ω @)s-ω0) Is frequency-shifted to the right by ω from the window function after the fast discrete Fourier transform0And (4) obtaining the product.
The phase of the higher harmonic to be measured is determined using the following formula:
Figure BDA0002506594350000082
in the formula (11), the reaction mixture,
Figure BDA0002506594350000083
is the phase of the higher harmonic to be measured, XWW (ω)0) Representing the maximum signal point at which the result of said convolution operation is maximum, arg being XWW (ω)0) The principal value of the phase angle of (c).
In order to more clearly illustrate steps 101-107, a specific example is provided below.
The carrier frequency of the PMW inverter is assumed to be 3000Hz, the grid frequency is approximate to the power frequency of 50Hz, and the signals are approximate to 60 cycles; sampling according to the frequency of 12.8kHz, which is equivalent to sampling 256 points per cycle of power frequency, and sampling 15360 points in total; taking a hanning window as an example, a hanning window with the width of 0.2s is adopted to process sampled signal points, and 2560 points are obtained by interception, and the cycle is approximately 10. Fig. 2a schematically shows 10 cycles of the harmonic signal acquired in the embodiment of the present application, and fig. 2b schematically shows 1 cycle of the harmonic signal acquired in the embodiment of the present application.
And performing fast discrete Fourier transform on the windowed signal points to obtain signal points subjected to fast discrete Fourier transform, and generating a more intuitive amplitude-frequency diagram according to the signal points subjected to the fast discrete Fourier transform. Fig. 3a schematically shows the amplitude-frequency diagram of the fundamental wave after the fast discrete fourier transform in the embodiment of the present application, and fig. 3b schematically shows the amplitude-frequency diagram of the main higher harmonic after the fast discrete fourier transform in the embodiment of the present application.
Finding out the frequency corresponding to the signal point with the maximum amplitude and the frequency corresponding to the adjacent signal point with larger amplitude from the amplitude-frequency diagram of the higher harmonic, taking the calculation of the 58 th harmonic as an example, finding out the frequency omega corresponding to the signal point with the maximum amplitude of the 58 th harmonicp1Frequency ω corresponding to 2 π × 580 and the adjacent larger amplitude signal pointsp2Taking H as 4, XWW (ω) is calculated according to equation (4) 2 pi × 579p1) And XWW (ω)p2). Fig. 4 is a schematic diagram illustrating a convolution result of a main higher harmonic after fast discrete fourier transform and a window function after continuous fourier transform in an embodiment of the present application. As shown in fig. 4, the abscissa indicates the harmonic degree of the higher harmonic, the ordinate indicates the convolution operation result, 4 signal points are exemplarily shown in the figure, the harmonic degree of the 1 st point is 55.97 (i.e., X is 55.97), the convolution result is 3.85 (i.e., Y is 3.85), the harmonic degree of the 2 nd point is 57.97 (i.e., X is 57.97), the convolution result is 6.879 (i.e., Y is 6.879), the harmonic degree of the 3 rd point is 61.96 (i.e., X is 61.96), the convolution result is 5.652 (i.e., Y is 5.652), the harmonic degree of the 4 th point is 63.96 (i.e., X is 63.96), and the convolution result is 3.752 (i.e., Y is 3.752).
The threshold value δ of | Δ ω | is set to 1e-6The learning rate η is set to 0.01, the initial value of the gradient ascent method is set according to the formula (8) and the formula (9), the update of ω is set according to the formula (5), the formula (6) and the formula (7), and ω is calculated02 pi × 579.68353. Will omega0The amplitude a is 36.72 and the phase is calculated by substituting the equation (10) and the equation (11), respectively
Figure BDA0002506594350000084
The frequency, amplitude and phase of the fundamental and the major harmonics are shown in Table 1, where the fundamental frequency is 49.99 Hz.
Table 1: one example of the frequency, amplitude and phase of the fundamental and the major higher harmonics
Figure BDA0002506594350000085
Figure BDA0002506594350000091
To describe the above more clearly, as shown in fig. 5, a general flowchart corresponding to a harmonic measurement method provided in the embodiment of the present application is shown. The method specifically comprises the following steps:
step 501, acquiring a high-order harmonic signal to be measured.
And 502, sampling the high-order harmonic signal to be measured according to a preset frequency.
Step 503, processing the sampled signal points by using a preset window function.
And step 504, performing fast discrete Fourier transform on the processed signal points.
And 505, performing continuous Fourier transform on a preset window function, and performing convolution operation on the window function subjected to the continuous Fourier transform and the signal points subjected to the fast discrete Fourier transform.
Step 506, finding out the frequency omega of the signal point with the maximum amplitude in the amplitude-frequency diagram generated by the signal points after the fast discrete Fourier transformp1And frequency omega of adjacent signal points with larger amplitudep2。
Step 507, at ωp1And omegap2Convolving the two frequencies with the window function after the continuous Fourier transform, and recording the result as XWW (omega)p1) And XWW (ω)p2)。
In step 508, the result obtained in step 507 is used to set an initial value for the gradient ascent operation.
In step 509, Δ ω (k) is calculated according to the update formula of the gradient ascent method.
Step 510, determining whether | Δ ω (k) | is greater than or equal to a threshold δ, and if so, executing step 511; otherwise, step 512 is performed.
In step 511, k is k +1, and step 509 and step 510 are executed again.
Step 512, using ω (k) when | Δ ω (k) | is smaller than the threshold δ as the frequency ω of the higher harmonic signal to be measured0。
513, according to the frequency ω of the higher harmonic signal to be measured0And the preset conversion relation among the frequency, the amplitude and the phase position to determine the amplitude A of the higher harmonic signal to be measured and the phase position of the higher harmonic signal to be measured
Figure BDA0002506594350000092
Therefore, in the embodiment of the application, the maximum value of the convolution operation result is solved by using a gradient ascent method, polynomial fitting is not involved in the process of circular calculation, only algebraic operation is involved, the operation complexity is low, meanwhile, a proper operation initial value is given, the range of the convolution operation is narrowed, the operation amount is reduced, the amplitude and the phase of the harmonic wave to be measured are calculated according to the convolution operation result and the frequency of the solved harmonic wave to be measured, the operation is simple and convenient, and the operation is easy to execute.
The following are embodiments of the apparatus of the present application that may be used to perform embodiments of the method of the present application. For details which are not disclosed in the embodiments of the apparatus of the present application, reference is made to the embodiments of the method of the present application.
Fig. 6 schematically shows a structural diagram of a measurement apparatus for higher harmonics according to an embodiment of the present application. As shown in fig. 6, the apparatus has a function of implementing the above-mentioned higher harmonic measurement method, and the function may be implemented by hardware, or by hardware executing corresponding software. The apparatus may include: an acquisition unit 601 and a processing unit 602.
An acquiring unit 601, configured to acquire a higher harmonic signal to be measured.
The processing unit 602 is configured to sample a to-be-measured higher harmonic signal according to a preset frequency to obtain a plurality of sampled signal points; processing the plurality of sampled signal points by adopting a preset window function to obtain a plurality of processed signal points; respectively carrying out fast discrete Fourier transform on the processed signal points to obtain a plurality of fast discrete Fourier transformed signal points; performing continuous Fourier transform on a preset window function, and performing convolution operation on the window function subjected to continuous Fourier transform and a plurality of signal points subjected to fast discrete Fourier transform to obtain a plurality of signal points subjected to convolution operation; determining a maximum signal point with the maximum convolution operation result value from the signal points after the convolution operation, and determining the frequency of the maximum signal point as the frequency of the high-order harmonic signal to be measured; and determining the amplitude of the high-order harmonic signal to be measured and the phase of the high-order harmonic signal to be measured according to the frequency of the high-order harmonic signal to be measured and the conversion relation between the preset frequency and the amplitude and the phase.
In one possible implementation, the plurality of sampled signal points is represented by the following formula:
Figure BDA0002506594350000101
where x (m Δ t) represents the sampled signal point, m is a natural number, Δ t is a discrete time interval, A is the amplitude of the higher harmonic signal to be measured, ω is0Is the frequency of the higher harmonic signal to be measured,
Figure BDA0002506594350000102
is the phase of the higher harmonic signal to be measured.
In a possible implementation manner, the width of the preset window function is:
T＝N×Δt
where T is the width of the preset window function, N is an even number, representing the number of signal points after processing, and Δ T is the discrete time interval.
In one possible implementation, the plurality of fft-ed signal points are determined using the following equation:
Figure BDA0002506594350000103
wherein, XW (n ω)s) Representing the signal points after the fast discrete Fourier transform, N is an integer between (-N/2) +1 and N/2, Z is an integer, N is an even number and represents the number of signal points after processing, omegasIs the frequency domain resolution, A is the amplitude of the higher harmonic signal to be measured, omega0Is the frequency of the higher harmonic signal to be measured,
Figure BDA0002506594350000108
is the phase of the higher harmonic signal to be measured, T is the width of the predetermined window function, j is the unit of imaginary number, W (n ωs) Representing a window function after a fast discrete Fourier transform, W (n ω @)s-ω0) Is frequency-shifted by ω from the window function after the fast discrete Fourier transform0And (4) obtaining the product.
In one possible implementation, the plurality of signal points after convolution operation are determined by the following formula:
Figure BDA0002506594350000104
XWW (omega) represents signal points after convolution operation, omega represents the frequency of any signal point after convolution operation, H is a positive integer, 2H +1 spectral lines need to cover the main lobe of the fast discrete Fourier transform of a preset window function, and XW (n omega) represents the frequency of any signal point after convolution operations) Representing signal points after a fast discrete Fourier transform, omegasIs the frequency domain resolution, T is the width of a preset window function, j is an imaginary unit, W (omega) represents the window function after continuous Fourier transform, W (omega-n omega)s) Is frequency-shifted by n omega to the right by the window function after the continuous Fourier transformsAnd (4) obtaining the product.
In one possible implementation, the amplitude of the higher harmonic to be measured is determined using the following formula:
Figure BDA0002506594350000105
where A is the amplitude of the higher harmonic to be measured, XWW (ω)0) Represents the maximum signal point, ω, at which the convolution result value is maximum0Is the frequency of the higher harmonic signal to be measured, H is a positive integer, 2H +1 spectral lines need to cover the main lobe after the fast discrete Fourier transform of a preset window function, omegasIs the frequency domain resolution, | | is the absolute value, W (n ω |)s) Representing a window function after a fast discrete Fourier transform, W (n ω @)s-ω0) Is frequency-shifted by ω from the window function after the fast discrete Fourier transform0And (4) obtaining the product.
The phase of the higher harmonic to be measured is determined by the following formula:
Figure BDA0002506594350000106
wherein the content of the first and second substances,
Figure BDA0002506594350000107
is the phase of the higher harmonic to be measured, XWW (ω)0) Representing the maximum signal point at which the convolution result has the largest value, arg is XWW (ω)0) The principal value of the phase angle of (c).
In a possible implementation manner, the processing unit 602 is specifically configured to:
and determining the maximum signal point with the maximum convolution operation result value from the plurality of signal points after convolution operation by adopting a gradient rising method.
In a possible implementation manner, the processing unit 602 is specifically configured to:
generating a signal amplitude-frequency diagram according to the signal points after the fast discrete Fourier transform; determining a first signal point with the maximum amplitude, a second signal point adjacent to the left of the first signal point and a third signal point adjacent to the right of the first signal point from the signal amplitude-frequency diagram; judging whether the amplitude of the second signal point is larger than or equal to the amplitude of the third signal point or not, and if the amplitude of the second signal point is larger than or equal to the amplitude of the third signal point, obtaining an operation initial value of a gradient rising method according to the frequency of the first signal point and the frequency of the second signal point; and if the amplitude of the second signal point is smaller than the amplitude of the third signal point, obtaining an operation initial value of the gradient rising method according to the frequency of the first signal point and the frequency of the third signal point.
Therefore, after the sampled signal time domain windowing function is subjected to fast discrete Fourier transform, convolution calculation is carried out with the continuous Fourier transform of the same window function, phase delay after the time domain windowing is offset at the frequency point of the higher harmonic signal to be measured, and the convolution reaches an extreme value.
In an exemplary embodiment, a computer-readable storage medium is further provided, in which a computer program or an intelligent contract is stored, and the computer program or the intelligent contract is loaded and executed by a node to implement the transaction processing method provided by the above-described embodiment. Alternatively, the computer-readable storage medium may be a Read-Only Memory (ROM), a Random Access Memory (RAM), a CD-ROM, a magnetic tape, a floppy disk, an optical data storage device, and the like.
Those skilled in the art will clearly understand that the techniques in the embodiments of the present application may be implemented by way of software plus a required general hardware platform. Based on such understanding, the technical solutions in the embodiments of the present application may be essentially implemented or a part contributing to the prior art may be embodied in the form of a software product, which may be stored in a storage medium, such as a ROM/RAM, a magnetic disk, an optical disk, etc., and includes several instructions for enabling a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method described in the embodiments or some parts of the embodiments of the present application.
Other embodiments of the disclosure will be apparent to those skilled in the art from consideration of the specification and practice of the disclosure disclosed herein. This application is intended to cover any variations, uses, or adaptations of the disclosure following, in general, the principles of the disclosure and including such departures from the present disclosure as come within known or customary practice within the art to which the disclosure pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the disclosure being indicated by the following claims.
It will be understood that the present disclosure is not limited to the precise arrangements described above and shown in the drawings and that various modifications and changes may be made without departing from the scope thereof. The scope of the present disclosure is limited only by the appended claims.

Claims (5)

1. A method for measuring higher harmonics, the method comprising:
acquiring a higher harmonic signal to be measured;
sampling the high-order harmonic signal to be measured according to a preset frequency to obtain a plurality of sampled signal points;
performing time domain windowing on the sampled signal points by adopting a preset window function to obtain a plurality of processed signal points;
respectively carrying out fast discrete Fourier transform on the processed signal points to obtain a plurality of fast discrete Fourier transformed signal points;
performing continuous Fourier transform on the preset window function, and performing convolution operation on the window function after the continuous Fourier transform and the signal points after the multiple fast discrete Fourier transforms to obtain multiple signal points after the convolution operation;
determining a maximum signal point with the maximum convolution operation result value from the signal points after the convolution operation, and determining the frequency of the maximum signal point as the frequency of the high-order harmonic signal to be measured;
determining the amplitude of the high-order harmonic signal to be measured and the phase of the high-order harmonic signal to be measured according to the frequency of the high-order harmonic signal to be measured and the conversion relation between the preset frequency and the amplitude and the phase; wherein:
the plurality of sampled signal points are represented by the following formula:
Figure FDA0003528208520000011
wherein x (m Δ t) represents the sampled signal point, m is a natural number, Δ t is a discrete time interval, A is the amplitude of the higher harmonic signal to be measured, ω is0Is the frequency of the higher harmonic signal to be measured,
Figure FDA0003528208520000012
is the phase of the higher harmonic signal to be measured;
the width of the preset window function is:
T＝N×Δt
wherein, T is the width of the preset window function, N is an even number and represents the number of the processed signal points, and delta T is a discrete time interval;
the plurality of signal points after the fast discrete fourier transform are determined using the following formula:
Figure FDA0003528208520000013
wherein, XW (n ω)s) Representing the signal points after the fast discrete Fourier transform, N is an integer between (-N/2) +1 and N/2, Z is an integer, N is an even number and represents the number of the signal points after the processing, omegasIs the frequency domain resolution, A is the amplitude of the higher harmonic signal to be measured, omega0Is the frequency of the higher harmonic signal to be measured,
Figure FDA0003528208520000015
is the phase of the higher harmonic signal to be measured, T is the width of the predetermined window function, j is the unit of imaginary number, W (n ωs) Representing a window function after a fast discrete Fourier transform, W (n ω @)s-ω0) Is frequency-shifted to the right by ω from the window function after the fast discrete Fourier transform0Obtaining;
the signal points after the convolution operation are determined by adopting the following formula:
Figure FDA0003528208520000014
XWW (omega) represents the signal point after the convolution operation, omega represents the frequency of any signal point after the convolution operation, H is a positive integer, 2H +1 spectral lines need to cover the main lobe of the fast discrete Fourier transform of the preset window function, and XW (n omega)s) Representing said signal points after said fast discrete Fourier transform, ωsIs the frequency domain resolution, T is the width of a preset window function, j is an imaginary unit, W (omega) represents the window function after continuous Fourier transform, W (omega-n omega)s) Is frequency-shifted by n omega to the right by the window function after the continuous Fourier transformsObtaining;
the amplitude of the higher harmonic to be measured is determined by the following formula:
Figure FDA0003528208520000021
where A is the amplitude of the higher harmonic to be measured, XWW (ω)0) Represents the maximum signal point, ω, at which the result of said convolution operation is maximum0Is the frequency of the higher harmonic signal to be measured, H is a positive integer, 2H +1 spectral lines need to cover the main lobe after the fast discrete Fourier transform of the preset window function, omegasIs the frequency domain resolution, | | is the absolute value, W (n ω |)s) Representing a window function after a fast discrete Fourier transform, W (n ω @)s-ω0) Is frequency-shifted by ω from the window function after the fast discrete Fourier transform0Obtaining the product;
the phase of the higher harmonic to be measured is determined by the following formula:
Figure FDA0003528208520000022
wherein the content of the first and second substances,
Figure FDA0003528208520000023
is the phase of the higher harmonic to be measured, XWW (ω)0) Representing the maximum signal point at which the result of said convolution operation is maximum, arg being XWW (ω)0) The principal value of the phase angle of (c).
2. The method of claim 1, wherein determining a maximum signal point from the plurality of convolved signal points at which a result of the convolution operation is largest comprises:
and determining the maximum signal point with the maximum convolution operation result value from the plurality of signal points after convolution operation by adopting a gradient rising method.
3. The method according to claim 2, wherein the operation initial value of the gradient ascent method is determined by:
generating a signal amplitude-frequency diagram according to the signal points after the plurality of fast discrete Fourier transforms;
determining a first signal point with the maximum amplitude, a second signal point adjacent to the left of the first signal point and a third signal point adjacent to the right of the first signal point from the signal amplitude-frequency diagram;
judging whether the amplitude of the second signal point is larger than or equal to the amplitude of the third signal point or not, and if the amplitude of the second signal point is larger than or equal to the amplitude of the third signal point, obtaining an operation initial value of the gradient rising method according to the frequency of the first signal point and the frequency of the second signal point;
and if the amplitude of the second signal point is smaller than that of the third signal point, obtaining an operation initial value of the gradient rising method according to the frequency of the first signal point and the frequency of the third signal point.
4. An apparatus for measuring higher harmonics, the apparatus comprising:
the acquisition unit is used for acquiring a to-be-measured higher harmonic signal;
the processing unit is used for sampling the higher harmonic signal to be measured according to a preset frequency to obtain a plurality of sampled signal points; performing time domain windowing on the sampled signal points by adopting a preset window function to obtain a plurality of processed signal points; respectively carrying out fast discrete Fourier transform on the processed signal points to obtain a plurality of fast discrete Fourier transformed signal points; performing continuous Fourier transform on the preset window function, and performing convolution operation on the window function after the continuous Fourier transform and the signal points after the fast discrete Fourier transform to obtain a plurality of signal points after the convolution operation; determining a maximum signal point with a maximum convolution operation result value from the signal points after the convolution operation, and determining the frequency of the maximum signal point as the frequency of the high-order harmonic signal to be measured; determining the amplitude of the high-order harmonic signal to be measured and the phase of the high-order harmonic signal to be measured according to the frequency of the high-order harmonic signal to be measured and the conversion relation between the preset frequency and the amplitude and the phase; wherein:
the plurality of sampled signal points are represented by the following formula:
Figure FDA0003528208520000024
wherein x (m Δ t) represents the sampled signal point, m is a natural number, Δ t is a discrete time interval, A is the amplitude of the higher harmonic signal to be measured, ω is0Is the frequency of the higher harmonic signal to be measured,
Figure FDA0003528208520000037
is the phase of the higher harmonic signal to be measured;
the width of the preset window function is:
T＝N×Δt
wherein, T is the width of the preset window function, N is an even number and represents the number of the processed signal points, and delta T is a discrete time interval;
the plurality of signal points after the fast discrete fourier transform are determined using the following formula:
Figure FDA0003528208520000031
wherein, XW (n ω)s) Representing the signal points after the fast discrete Fourier transform, N is an integer between (-N/2) +1 and N/2, Z is an integer, N is an even number and represents the number of the signal points after the processing, omegasIs the frequency domain resolution, A is the amplitude of the higher harmonic signal to be measured, omega0Is the frequency of the higher harmonic signal to be measured,
Figure FDA0003528208520000032
is the phase of the higher harmonic signal to be measured, T is the width of the predetermined window function, j is the unit of imaginary number, W (n ωs) Representing a window function after a fast discrete Fourier transform, W (n ω @)s-ω0) Is frequency-shifted by ω from the window function after the fast discrete Fourier transform0Obtaining;
the signal points after the convolution operation are determined by adopting the following formula:
Figure FDA0003528208520000033
XWW (omega) represents the signal point after the convolution operation, omega represents the frequency of any signal point after the convolution operation, H is a positive integer, 2H +1 spectral lines need to cover the main lobe of the fast discrete Fourier transform of the preset window function, and XW (n omega)s) Representing said signal points after fast discrete Fourier transform, ωsIs the frequency domain resolution, T is the width of a preset window function, j is an imaginary unit, W (omega) represents the window function after continuous Fourier transform, W (omega-n omega)s) Is frequency-shifted by n omega to the right by the window function after the continuous Fourier transformsObtaining;
the amplitude of the higher harmonic to be measured is determined by the following formula:
Figure FDA0003528208520000034
where A is the amplitude of the higher harmonic to be measured, XWW (ω)0) Represents the maximum signal point, ω, at which the convolution result value is maximum0Is the frequency of the higher harmonic signal to be measured, H is a positive integer, 2H +1 spectral lines need to cover the main lobe after the fast discrete Fourier transform of the preset window function, omegasIs the frequency domain resolution, | | is the absolute value, W (n ω |)s) Representing a window function after a fast discrete Fourier transform, W (n ω @)s-ω0) Is frequency-shifted by ω from the window function after the fast discrete Fourier transform0Obtaining;
the phase of the higher harmonic to be measured is determined by the following formula:
Figure FDA0003528208520000035
wherein the content of the first and second substances,
Figure FDA0003528208520000036
is the phase of the higher harmonic to be measured, XWW (ω)0) Representing the maximum signal point at which the result of said convolution operation is maximum, arg being XWW (ω)0) The principal value of the phase angle of (c).
5. The apparatus according to claim 4, wherein the processing unit is specifically configured to:
and determining the maximum signal point with the maximum convolution operation result value from the plurality of signal points after convolution operation by adopting a gradient rising method.
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