CN112346875B - Estimation method of parallelization logarithmic uniform power spectrum - Google Patents
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Abstract
The invention belongs to the technical field of measurement, and discloses a method for estimating a parallelization logarithmic uniform power spectrum, which comprises the following steps: (1) Selecting logarithmic frequency points to be calculated for spectrum estimation, and obtaining frequency resolution according to frequency; (2) Performing parallelized single-point Fourier transform on the frequency resolution; (3) And obtaining the power spectrum density according to the Fourier transform result, and obtaining the spectrum estimated value corresponding to the current frequency point after averaging the estimated values of the multi-section spectrum density. The invention can realize the calculation of the power spectrum of more data in the same time, and the higher the data quantity is, the higher the resolution of the power spectrum is, so as to obtain higher resolution.
Description
Technical Field
The invention belongs to the technical field of measurement, and particularly relates to an estimation method of a parallelization logarithmic uniform power spectrum.
Background
The power spectrum estimation is widely applied to measurement and test processes in various fields, such as instrument noise background analysis, identification of system amplitude-frequency response and the like. Common methods of power spectrum estimation such as periodogram and modified periodogram methods, which are based on fast fourier transforms, result in uniform frequency-point linearity. For most signals, the bandwidth spans multiple orders of magnitude of frequency, and a linear uniform frequency point will result in a drawn power spectral density curve that is data intensive at high frequencies, with large amplitude fluctuations and low accuracy.
In order to solve the problem that the data points of the spectral density curve at high frequencies are too dense and the accuracy is not high, document Improved spectrum estimation from digitized time series on a logarithmic frequency axis proposes a method for estimating the power spectrum at logarithmically uniform frequency points. The method fully utilizes the relation between the frequency resolution and the amplitude precision, so that the spectrum estimation result can reach enough resolution at low frequency, the spectrum density estimation precision in a high frequency range can be improved, the frequency points are approximately even in logarithm, and a good visual effect can be achieved when drawing in a logarithmic coordinate.
The method for estimating the power spectrum with even logarithm cannot be supported by the fast Fourier transform (because the traditional power spectrum estimation uses the fast Fourier transform and the method is parallelized, the method cannot use the fast Fourier transform, the calculation process cannot call the fast Fourier transform to carry out core operation), and serial calculation is adopted, so that multiple CPU cores of a computer cannot be fully utilized, the calculation efficiency is low, and the time consumption is long and the speed is low when processing a large amount of data.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a method for estimating a parallelization logarithmic uniform power spectrum, and aims to solve the problems of long time consumption and low speed when processing a large amount of data caused by the fact that fast Fourier transform cannot be called for core operation in the prior art.
The invention provides an estimation method of a parallelization logarithmic uniform power spectrum, which comprises the following steps:
(1) Selecting logarithmic frequency points to be calculated for spectrum estimation, and obtaining frequency resolution according to frequency;
(2) Performing parallelized single-point fourier transform on the frequency resolution;
(3) And obtaining the power spectrum density according to the Fourier transform result, and obtaining the spectrum estimated value corresponding to the current frequency point after averaging the estimated values of the multi-section spectrum density.
The selection of the logarithmic frequency points is realized by adopting a serial calculation mode, and the serial calculation does not affect the overall calculation efficiency because the part has a simple calculation structure and small data volume.
Further, the step (1) specifically includes:
(1.1) calculating the relation between the frequency resolution and the frequency according to the given expected frequency points;
(1.2) calculating the frequency resolution corresponding to the frequency in order from the minimum frequency point, and correcting the frequency resolution.
Further, the step (1.1) specifically comprises: for preset J des And sampling the frequency points with even logarithm to obtain N frequency data, and calculating the frequency resolution.
Further, the step (1.2) specifically comprises:
(1.2.1) counting the frequency points J des Ordering is performed and the minimum frequency point is obtained,
(1.2.2) when the frequency does not reach the Nyquist frequency in order from the minimum frequency point, according to the formulaCalculating the frequency resolution;
(1.2.3) modifying the frequency resolution;
wherein r is 0 (j) The frequency resolution corresponding to the jth frequency f (j).
Still further, the principle of correcting the frequency resolution in the step (1.2.3) includes: (a) The calculated value of the frequency resolution cannot be smaller than the limit of the minimum resolution in the discrete fourier transform; (b) The frequency resolution should ensure that the ratio of the upper frequency limit to the frequency resolution is an integer to facilitate segmentation.
Further, the correction of the frequency resolution in the step (1.2.3) is specifically:
calculating the frequency resolution corresponding to the frequency point, and when the frequency resolution is smaller than the minimum resolution r min When it is, it is corrected to the minimum resolution;
according to the formulaPerforming second correction on the frequency resolution;
wherein r is avg For average resolution, r 0 (j) For the frequency resolution corresponding to the jth frequency f (j), r min R is the minimum resolution min ＝f s /N，f s For the sampling rate, N is the number of frequencies employed.
Further, the resolution after the second correction is calculated again by solving the number of segmentation points and rounding down, and the resolution after the final correction is obtained.
Wherein, GPU can be adopted to realize single-point Fourier transform, thereby improving local calculation efficiency.
The GPU can be adopted to estimate the spectral density of each frequency point, so that the overall calculation efficiency is greatly improved.
The method comprises the steps of estimating logarithmic frequency points to be calculated by selecting a frequency spectrum, and obtaining frequency resolution according to the frequency; performing parallelized single-point Fourier transform on the frequency resolution; obtaining power spectrum density according to the Fourier transform result, and obtaining a spectrum estimated value corresponding to the current frequency point after averaging the estimated values of the multi-section spectrum density; the power spectrum of more data can be calculated in the same time, and the resolution of the power spectrum is higher as the data quantity is larger, so that the higher resolution is obtained.
Drawings
Fig. 1 is a block flow diagram of an implementation of a method for estimating a parallel log uniform power spectrum according to an embodiment of the present invention.
Fig. 2 is an effect diagram of power spectrum estimation by using the method for estimating the parallelized log-uniform power spectrum provided by the embodiment of the invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
The method for estimating the parallel logarithmic uniform power spectrum is suitable for various occasions needing to estimate the power spectrum. According to the method, the optimization acceleration is carried out on the estimation method of the log-uniform power spectrum through serial calculation, parallel operation is carried out on the core part of the method for solving the single-point power spectrum through multiple CPUs/GPUs, and the power spectrum with higher resolution can be obtained in the same time through improvement of the calculation efficiency.
The method for estimating the parallel logarithmic uniform power spectrum mainly comprises the following steps: a logarithmic frequency point selection method, a parallelized single-point fourier transform method, and a spectral density estimation method. The logarithmic frequency point selection method can adopt basic serial calculation, and the serial method of the part has negligible influence on the overall calculation efficiency due to the simple calculation structure and small data volume of the part. The single-point Fourier transform can be converted into matrix calculation, and further, GPU (graphics processing unit) can be adopted for calculation, and the GPU is a parallelization calculation mode when processing information, so that the local calculation efficiency can be improved. When the spectral density estimation is carried out on each frequency point, CPU parallel calculation can be adopted, the CPU parallel calculation efficiency is related to the CPU performance, and the calculation efficiency can be greatly improved by adopting a multi-core CPU.
Since the frequency points of the method are uniformly distributed in a logarithmic scale, the frequency interval, i.e., the frequency resolution, between every two adjacent frequency points is different. Under the condition of even logarithm, the proportional relation between the frequency resolution and the current frequency value is easy to deduce. The frequency resolution versus frequency is calculated from a given number of desired frequency points. Then, starting from the minimum frequency point, calculating the frequency resolution corresponding to the frequency, and correcting the frequency resolution.
First input setting J des The frequency points with even logarithm are sampled, N data are obtained, the Nyquist frequency is half of the sampling rate and f is the frequency of the sampling s 2, which is also the maximum frequency point of the power spectrum, the frequency resolution r corresponding to the jth frequency f (j) 0 (j) Is (S5):
the correction of the frequency resolution needs to satisfy two conditions: firstly, the calculated value of the frequency resolution cannot be smaller than the limit of the minimum resolution in the discrete Fourier transform, and if the calculated value is smaller than the theoretical value, the theoretical value is needed to be taken; secondly, the ratio of the upper frequency limit to the frequency resolution is ensured to be an integer so as to be convenient for segmentation, and if the condition is not met, the frequency resolution is subjected to micro-correction so as to meet the condition.
The correction of the frequency resolution can be specifically performed according to the following steps, firstly, after the corresponding resolution is calculated by the frequency point, whether the frequency point is larger than the theoretical minimum resolution r is judged min ＝f s If it is smaller than the value, it is corrected to the minimum resolution. Then, canSetting the average resolution r by man avg The frequency resolution is modified a second time as follows, with a better transition between low and high frequencies:
finally, the integer segmentation requirement needs to be met, specifically, the segmentation point number can be calculated by solving the resolution after the second correction, rounding down, and then recalculating the resolution to obtain the resolution after the final correction. The formula is as follows:
and adding the corrected frequency resolution to the current frequency to obtain a next frequency point, and repeating the above processes until the frequency reaches the Nyquist frequency. Finally, the frequency points are summarized to obtain the frequency points needed to be calculated in spectrum estimation, and the frequency points after the summarization are usually less than the frequency points which are expected to be set, because the correction of the frequency resolution makes the distribution of the frequency points not strictly equal in logarithm.
After obtaining the frequency resolution, dividing the task of calculating the power spectrum into a plurality of cores by using a CPU parallelization method, independently calculating the segmentation times corresponding to the current frequency point by each core, preprocessing each segment of data according to the set overlapping rate and the calculated segmentation times, wherein linear drift removal, windowing functions and the like are included, and dividing the data into K (j) segments according to the frequency resolution r (j) corresponding to the j-th frequency point, wherein the first data after preprocessing of the K-th segment is G (j, K, l).
Then single-point Fourier transform is carried out, namelyThis process may be converted to a matrix multiplied form and may be accelerated by the GPU. The single-point Fourier transform result can be converted into power spectral density according to wiener Xin Qin formula, and the estimated values of multiple sections of spectral density are averaged to obtain the corresponding current frequency pointThe spectral estimate of (2) is:for the power spectral density, the normalized coefficient C is related to the window function w (l), specifically:and summarizing the calculated frequency points and the power spectrum density values to finish the calculation. And the output can be accomplished graphically.
In order to further explain the method for estimating the parallel logarithmic uniform power spectrum provided by the embodiment of the invention, the following details are described with reference to the accompanying drawings and with reference to specific examples:
as shown in fig. 1, the method for estimating the parallel logarithmic uniform power spectrum provided by the embodiment of the invention comprises the following steps:
s1: input demand frequency Point J des ；
S2: counting the frequency points J des Sequencing and obtaining a minimum frequency point;
s3: judging whether the Nyquist frequency is reached, if so, turning to step S4; if not, turning to step S5;
s4: inputting data;
s5, performing S5; calculating frequency resolution;
s6: correcting frequency resolution;
s7: calculating the next frequency point, and returning to the step S3;
s8: taking a first frequency point;
s9: calculating the segmentation times;
s10: preprocessing each segment of data;
s11: single-point fourier transform;
s12: calculating the power spectrum density of each section;
s13: taking a multi-section spectrum density average value;
s14: judging whether the last frequency point is reached, if so, turning to step S16; if not, go to step S15;
s15: taking down a frequency point and transferring to step S9;
s16: results were summarized and plotted.
Fig. 2 shows the result of power spectrum estimation by using the parallel logarithmic uniform power spectrum estimation method provided by the embodiment of the invention.
It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (9)
1. The method for estimating the parallel logarithmic uniform power spectrum is characterized by comprising the following steps of:
(1) Calculating the relation between the frequency resolution and the frequency according to the given expected frequency points, sequentially calculating the frequency resolution corresponding to the frequency from the minimum frequency point, and correcting the frequency resolution to obtain the frequency resolution;
(2) After obtaining the frequency resolution, dividing the task of calculating the power spectrum into a plurality of cores by using a CPU parallelization method, independently calculating the segmentation times corresponding to the current frequency point by each core, preprocessing each segment of data according to the set overlapping rate and the calculated segmentation times, and then performing single-point Fourier transform;
(3) And converting the single-point Fourier transform result into power spectral density according to a wiener Xin Qin formula, averaging the estimated values of the multi-section spectral density to obtain a frequency spectrum estimated value corresponding to the current frequency point, and summarizing the calculated frequency point and the power spectral density value.
2. The estimation method of claim 1, wherein the selection of logarithmic frequency bins is accomplished by means of serial computation.
3. The estimation method according to claim 1, wherein the step (1.1) is specifically: for preset J des And sampling the frequency points with even logarithm to obtain N frequency data, and calculating the frequency resolution.
4. The estimation method according to claim 3, wherein the step (1.2) is specifically:
(1.2.1) counting the frequency points J des Ordering is performed and the minimum frequency point is obtained,
(1.2.2) when the frequency does not reach the Nyquist frequency in order from the minimum frequency point, according to the formulaCalculating the frequency resolution;
(1.2.3) modifying the frequency resolution;
wherein r is 0 (j) The frequency resolution corresponding to the jth frequency f (j).
5. The estimation method of claim 4, wherein the principle of correcting the frequency resolution in the step (1.2.3) includes: (a) The calculated value of the frequency resolution cannot be smaller than the limit of the minimum resolution in the discrete fourier transform; (b) The frequency resolution should ensure that the ratio of the upper frequency limit to the frequency resolution is an integer to facilitate segmentation.
6. The estimation method according to claim 5, wherein the correction of the frequency resolution in the step (1.2.3) is specifically:
calculating the frequency resolution corresponding to the frequency point, and when the frequency resolution is smaller than the minimum resolution r min ＝f s at/N, correcting it to minimum resolution;
according to the formulaPerforming second correction on the frequency resolution;
wherein r is avg For average resolution, r 0 (j) For the frequency resolution corresponding to the jth frequency f (j), r min R is the minimum resolution min ＝f s /N，f s Is sampling rate, N is samplingThe number of frequencies used.
7. The estimation method of claim 6, wherein the final corrected frequency resolution is obtained by calculating the number of segmentation points for the second corrected resolution and rounding down the number of segmentation points and then recalculating the resolution.
8. The estimation method according to any of the claims 1-7, wherein a GPU is used for performing a single point fourier transform.
9. The estimation method according to any one of claims 1-7, wherein the spectral density estimation for each frequency bin is implemented using a GPU.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102624468A (en) * | 2011-12-30 | 2012-08-01 | 成都中安频谱科技有限公司 | Automatic broadband detection method based on dual fast Fourier transformation (FFT) |
| CN106970265A (en) * | 2017-03-29 | 2017-07-21 | 湖南工业大学 | A kind of method that incomplete S-transformation of use Multiple Time Scales estimates harmonic parameters |
| JP2020010195A (en) * | 2018-07-09 | 2020-01-16 | 三菱電機株式会社 | Frequency estimation device and tracking receiver |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN102624468A (en) * | 2011-12-30 | 2012-08-01 | 成都中安频谱科技有限公司 | Automatic broadband detection method based on dual fast Fourier transformation (FFT) |
| CN106970265A (en) * | 2017-03-29 | 2017-07-21 | 湖南工业大学 | A kind of method that incomplete S-transformation of use Multiple Time Scales estimates harmonic parameters |
| JP2020010195A (en) * | 2018-07-09 | 2020-01-16 | 三菱電機株式会社 | Frequency estimation device and tracking receiver |
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| Title |
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| 下一代重力卫星新型无拖曳与姿态控制系统研究;李洪银;博士电子期刊出版信息;全文 * |
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