CN118211011B - DFT calculation method and device for non-integer period sampling - Google Patents
DFT calculation method and device for non-integer period sampling Download PDFInfo
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Abstract
The invention relates to the technical field of radio frequency signal processing, in particular to a DFT calculation method and device for sampling in an irregular period. The method comprises the following steps: sampling the radio frequency signal according to a preset sampling frequency to obtain non-whole period sampling data; for each period of the radio frequency signal, acquiring a sampling value in the period corresponding to a sampling point in the period, and performing DFT calculation on the sampling value in the period to obtain a first signal parameter value; acquiring a sampling value corresponding to a sampling point after the last sampling point of the period as an supplementing sampling value, combining the sampling value in the period with the supplementing sampling value, and performing DFT calculation to obtain a second signal parameter value; and obtaining a corrected signal parameter value after carrying out weighted summation on the first signal parameter value and the second signal parameter value. The method effectively reduces the fluctuation caused by frequency spectrum leakage, has a simple calculation formula, small calculation delay, less hardware consumption and cost reduction.
Description
Technical Field
The invention relates to the technical field of radio frequency signal processing, in particular to a DFT calculation method and device for sampling in an irregular period.
Background
The radio frequency power supply calculates forward power and reflected power through output voltage and current. If the voltage and current acquisition error fluctuation is large, the calculated result of the whole system cannot meet the high requirement of the radio frequency power supply on the precision, such as the great influence on the yield of the produced chips. The sampling rate of the current high-speed ADC is above 50MHz, the radio frequency is 10 times lower than the sampling rate, and the fixed frequency sampling is used, so that the use of a phase-locked loop and a programmable crystal oscillator is reduced, and the cost is reduced. However, spectrum leakage is caused, for the spectrum leakage, a common processing mode is adopted, a window function is added to reduce the spectrum leakage, but the window function is selected in a plurality of ways, the realization is complex, the result is delayed to be output, and the closed loop adjustment is influenced.
Radio frequency of radio frequency power supplyIt can be provided to calculate the amplitude phase using DFT, to reduce the cost, using a fixed sampling frequencyIf (if)Is thatFrequency spectrum leakage occurs, resulting in periodic fluctuations in the calculation result.
Disclosure of Invention
Aiming at the problem of spectrum leakage and larger error of calculation results, the invention provides a DFT calculation method and device for sampling in a non-whole period.
In order to achieve the above object, the following technical solutions are proposed:
A DFT calculation method for sampling non-whole period includes the following steps:
Sampling the radio frequency signal according to a preset sampling frequency to obtain sampling data, wherein the sampling data are non-whole period sampling data;
For each period of the radio frequency signal,
Acquiring a sampling value in a period corresponding to a sampling point in the period, and performing DFT calculation on the sampling value in the period to obtain a first signal parameter value;
acquiring a sampling value corresponding to a sampling point after the last sampling point of the period as an supplementing sampling value, combining the sampling value in the period with the supplementing sampling value, and performing DFT calculation to obtain a second signal parameter value;
And obtaining a corrected signal parameter value after carrying out weighted summation on the first signal parameter value and the second signal parameter value.
Preferably, the obtaining the supplementary sampling value includes obtaining a sampling value corresponding to a sampling point closest to the last sampling point of the period as the supplementary sampling value.
Preferably, the calculation formula of the first signal parameter value is:
The real part is:
the imaginary part is:
Where w is the fundamental angular frequency, N is the integer part of the multiple of the first signal parameter value, N ε N, a k and b k are called Fourier coefficients, k is the harmonic order, Is the sampled data.
Preferably, the calculation formula of the second signal parameter value is:
The real part is:
the imaginary part is:
Where w is the fundamental angular frequency, N is the integer part of the multiple value in the first signal parameter value, N ε N, a k and b k are called Fourier coefficients, k is the harmonic order, Is the sampled data.
Preferably, the corrected signal parameter value is:
The real part is:
the imaginary part is:
Where w is the fundamental angular frequency, N is the integer part of the multiple value in the first signal parameter value, N ε N, a k and b k are called Fourier coefficients, k is the harmonic order, For sampling data, Y is the fractional part of the multiple value in the first signal parameter value.
As a preferred scheme, the corrected signal parameter value is adopted to calculate the amplitude of the corrected radio frequency signal, and the calculation formula is as follows:
Wherein a k is the amplitude of the corrected radio frequency signal, a 0 corresponds to the dc component of the radio frequency signal when k=0, a 1 is the fundamental component when n=1, a 2 is the second harmonic component when n=2, and a k is the real part of the complex number obtained by performing time-domain to frequency-domain conversion on the sampled signal by discrete fourier transform; b k performing a time-domain to frequency-domain transform on the sampled signal with a discrete fourier transform to obtain the imaginary part in the complex number.
Preferably, when the first signal parameter value and the second signal parameter value are weighted and summed, the coefficient corresponding to the first signal parameter value is a first coefficient, and the range of the first coefficient is 0 to 1; the second signal parameter value corresponds to a coefficient that is a second coefficient, the second coefficient ranges from 0 to 1, and the sum of the first coefficient and the second coefficient is 1.
Based on the same conception, a DFT computing device for sampling non-whole period is also provided, which comprises at least one processor and a memory in communication connection with the at least one processor; the memory stores instructions executable by the at least one processor to enable the at least one processor to perform a DFT calculation method of non-integer period sampling as described in any one of the preceding claims.
Compared with the prior art, the invention has the beneficial effects that: the method can effectively reduce the fluctuation caused by frequency spectrum leakage, has simple calculation formula, small calculation delay, less hardware and reduced cost.
Drawings
FIG. 1 is a flowchart of a DFT calculation method for sampling non-whole period in the embodiment 1;
FIG. 2 is a schematic diagram of DFT sliding calculation in example 1;
Fig. 3 is an example of sampling cases corresponding to sampling the radio frequency signal in the non-whole period of the time domain in embodiment 1;
fig. 4 is the result of amplitude calculation when the sliding filter is set to 147 points in embodiment 1;
fig. 5 is the result of amplitude calculation when the sliding filter is set to 148 points in embodiment 1;
FIG. 6 is a graph showing the result of the weighted calculation in example 1;
FIG. 7 is a diagram showing the result of the 32-point DFT sliding calculation in example 2;
FIG. 8 is a diagram showing the result of the 33-point DFT sliding calculation in example 2;
FIG. 9 is a graph showing comparison of DFT sliding calculation results in example 2.
Detailed Description
The present invention will be described in further detail with reference to test examples and specific embodiments. It should not be construed that the scope of the above subject matter of the present invention is limited to the following embodiments, and all techniques realized based on the present invention are within the scope of the present invention.
Example 1
A DFT calculation method for sampling non-whole period includes the following steps:
Sampling the radio frequency signal according to a preset sampling frequency to obtain sampling data, wherein the sampling data are non-whole period sampling data; the frequency employed here is preferably the ADC sampling frequency.
For each period of the radio frequency signal, acquiring a sampling value in a period corresponding to a sampling point in the period, and performing DFT calculation on the sampling value in the period to obtain a first signal parameter value; acquiring a sampling value corresponding to a sampling point after the last sampling point of the period as an supplementing sampling value, combining the sampling value in the period with the supplementing sampling value, and performing DFT calculation to obtain a second signal parameter value;
And obtaining a corrected signal parameter value after carrying out weighted summation on the first signal parameter value and the second signal parameter value.
Here, the non-integer period sampling means that the multiple value obtained by dividing the sampling frequency by the radio frequency is not an integer, and thus the obtained sampling data is non-integer period sampling data.
The acquiring the sampling value corresponding to the sampling point after the last sampling point of the period as the supplementary sampling value comprises acquiring the sampling value corresponding to the first sampling point after the last sampling point of the period as the supplementary sampling value.
The signal parameters in the calculation include amplitude and phase.
In the DFT calculation, the sampling signal is transformed from time domain to frequency domain by discrete Fourier transform, and in the obtained complex number,
The real part is:
the imaginary part is:
Where w is the fundamental angular frequency, N is the integer fraction of the multiple value in the first signal parameter value, N is the integer fraction of the multiple value in the second signal parameter value plus 1, a k and b k are called fourier coefficients, and k is the harmonic order.
When the first signal parameter is the first signal amplitude and the second signal parameter is the second signal amplitude, the first signal amplitude or the second signal amplitude calculation formula is:
Wherein a k is the amplitude of the fundamental wave parameter, a 0 corresponds to the direct current component of the radio frequency signal when k=0, a 1 is the fundamental wave component when n=1, a 2 is the second harmonic component when n=2, a k is the k harmonic amplitude, and a k is the real part of the complex number obtained by performing time-domain to frequency-domain conversion on the sampled signal by discrete fourier transform; b k performing a time-domain to frequency-domain transform on the sampled signal with a discrete fourier transform to obtain the imaginary part in the complex number.
When the first signal parameter and the second signal parameter are weighted and summed, the coefficient corresponding to the first signal parameter is a first coefficient, and the range of the first coefficient is 0 to 1 (the decimal part of 1-times value); the second signal parameter corresponds to a second coefficient ranging from 0 to 1 (1-first coefficient), i.e. the sum of the first coefficient and the second coefficient is 1.
When the first signal parameter is a first signal amplitude, the range of the first coefficient is 0-1; when the second signal parameter is the second signal amplitude, the range of the second coefficient is 0-1 (1-first coefficient).
When the first signal parameter is a first signal amplitude, the first coefficient is 0.72; when the second signal parameter is the second signal amplitude, the second coefficient is 0.28.
Example 2
When the radio frequency signal is converted from the time domain to the frequency domain, discrete frequency domain signals are generated by adopting DFT sliding calculation, a schematic diagram of the DFT sliding calculation is shown as shown in fig. 2, the radio frequency signals are collected through a high-speed ADC, two orthogonal signals of sin (down) and cos (down) are multiplied by the collected signals, namely, in one path, the input parameter a is assigned as the collected signals, b is assigned as sin (down), the output parameter u is equal to a multiplied by b, the output parameter u is the orthogonal signals of the collected signals multiplied by sin (down), in the other path, the input parameter a is assigned as the collected signals, b is assigned as cos (down), the output parameter u is equal to a multiplied by b, and the output parameter u is the orthogonal signals of the collected signals multiplied by cos (down). Wherein N is the number of periodic samples, N is the number of sampling points, k is the harmonic frequency, the frequency of the radio frequency signal is fr, the sampling frequency fs, w=2 pi fr/fs, the unit period Ts, ts=1/fs. Z (-N) delays the calculated value by N unit periods, ak and bk are added with a new value in each unit period, and the old values of the previous N periods are subtracted. And outputting DFT calculation results of the first N sampling points corresponding to the current period in each unit period. N in fig. 2 is also the sliding DFT window value.
When the fundamental wave amplitude is calculated, the calculation formula is as follows:
（1）
(2)
(3)
(4)
(5)
(6)
The INT () function is an integer-taking function, and is shown in fig. 3, for example, in fig. 3, where the abscissa is the number of samples, and the ordinate is the value obtained by normalizing the amplitude, where the sampling rate is 65M, the signal frequency is 440k, and the number of sampling points is 65M/0.44 m= 147.72. If the DFT calculation is performed in a rounding manner, there are two rounding results, 147 points and 148 points.
When the sliding filter is set to 147 points, the magnitude calculation result is shown in fig. 4, and as can be understood from fig. 4, the fluctuation is: 1.005-0.995=0.01.
When the sliding filter is set to 148 points, the magnitude calculation result is shown in fig. 5, and as can be seen from fig. 5, the fluctuation is: 1.0015-0.9985=0.003.
Based on the calculation results, two results are weighted, for example: 0.28 times the 147 points amplitude and 0.72 times the 148 points amplitude are added. The result of the amplitude calculation is shown in fig. 6.
The calculation formula is as follows:
（7）
（8）
the weighted calculation fluctuation is: 1.000057-0.999954 = 0.000103, the fluctuation is reduced by a factor of 30.
When the signal frequency is 2M, the sampling point number is 65M/2 m=32.5, the weighting calculation is performed on 32 points and 33 points, and the amplitude calculation results are shown in fig. 7, 8 and 9.
In fig. 7, 8 and 9, the fluctuation of the result calculated from 32 points was 0.03, the fluctuation of the result calculated from 33 points was 0.03, and the result calculated by weighting was 0.003. It can be seen that the frequency spectrum leakage degree is different between 2M and 400K due to the fact that the sampling points of one period are different, and the more the points are, the smaller the leakage is. Therefore, the higher the sampling rate, the better the DFT calculation is.
In the field of radio frequency power supply, the invention uses non-whole period sampling, discards the traditional window function mode based on frequency domain to cope with spectrum leakage, carries out weighted addition on the result through multiple DFT calculation (preferably twice), reduces spectrum leakage and reduces fluctuation.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, and alternatives falling within the spirit and principles of the invention.
Claims (4)
1. The DFT calculation method for sampling the non-whole period is characterized by comprising the following steps of:
Sampling the radio frequency signal according to a preset sampling frequency to obtain sampling data, wherein the sampling data are non-whole period sampling data;
For each period of the radio frequency signal,
Acquiring a sampling value in a period corresponding to a sampling point in the period, and performing DFT calculation on the sampling value in the period to obtain a first signal parameter value;
acquiring a sampling value corresponding to a sampling point after the last sampling point of the period as an supplementing sampling value, combining the sampling value in the period with the supplementing sampling value, and performing DFT calculation to obtain a second signal parameter value;
the first signal parameter value and the second signal parameter value are weighted and summed to obtain a corrected signal parameter value;
The calculation formula of the first signal parameter value is as follows:
The real part is:
the imaginary part is:
the calculation formula of the second signal parameter value is as follows:
The real part is:
the imaginary part is:
The corrected signal parameter values are:
The real part is:
the imaginary part is:
Where w is the fundamental angular frequency, N is the integer part of the multiple value in the first signal parameter value, N ε N, a k and b k are called Fourier coefficients, k is the harmonic order, For the sampled data, Y is the fractional part of the multiple value in the first signal parameter value;
The obtaining of the supplementary sample value includes obtaining a sample value corresponding to a closest sample point after a last sample point of the period as the supplementary sample value.
2. The DFT computation method of claim 1 wherein said corrected signal parameter value is used to compute the corrected rf signal amplitude by the following equation:
Wherein a k is the amplitude of the corrected radio frequency signal, a 0 corresponds to the direct current component of the radio frequency signal when k=0, a 1 is the fundamental component when n=1, a 2 is the second harmonic component when n=2, and a k is the real part of the complex number obtained by performing time-domain to frequency-domain conversion on the radio frequency signal by discrete fourier transform; b k performs a time-domain to frequency-domain transform on the sampled signal with a discrete fourier transform, resulting in an imaginary part in the complex number.
3. A method of DFT computation of non-integer periodic samples according to any of claims 1-2, wherein when said first signal parameter value and said second signal parameter value are weighted and summed, the coefficient corresponding to said first signal parameter value is a first coefficient, the first coefficient being in the range of 0 to 1; the second signal parameter value corresponds to a coefficient that is a second coefficient, the second coefficient ranges from 0 to 1, and the sum of the first coefficient and the second coefficient is 1.
4. A non-full period sampled DFT computing device comprising at least one processor, and a memory communicatively coupled to said at least one processor; the memory stores instructions executable by the at least one processor to enable the at least one processor to perform a non-integer period sampled DFT calculation method as claimed in any one of claims 1 to 3.
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| CN105137185A (en) * | 2015-07-23 | 2015-12-09 | 河海大学 | Frequency domain interpolation electric power harmonic wave analysis method based on discrete Fourier transform |
| CN109358223A (en) * | 2018-09-29 | 2019-02-19 | 海特尔机电工程技术（马鞍山）有限公司 | A kind of sliding window DFT harmonic current detecting method and device, storage medium |
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| CN114069660B (en) * | 2020-07-31 | 2024-08-09 | 金风科技股份有限公司 | Method and equipment for calculating harmonic waves of energy storage system |
| CN115219968A (en) * | 2021-04-14 | 2022-10-21 | 西门子(深圳)磁共振有限公司 | Method, device, system and storage medium for reducing radio frequency interference |
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| CN105137185A (en) * | 2015-07-23 | 2015-12-09 | 河海大学 | Frequency domain interpolation electric power harmonic wave analysis method based on discrete Fourier transform |
| CN109358223A (en) * | 2018-09-29 | 2019-02-19 | 海特尔机电工程技术（马鞍山）有限公司 | A kind of sliding window DFT harmonic current detecting method and device, storage medium |
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