Spectrum analysis sampling method based on Gaussian Seidel iteration and storage medium

Abstract

The invention relates to a spectral analysis sampling method based on Gaussian Seidel iteration and a storage medium, and belongs to the technical field of radio frequency microwaves, and the method comprises the steps: obtaining radio frequency microwave time domain signal data, and judging whether the time interval of the time domain signal data is uniform or not; performing data processing on the time domain signal data with the non-uniform time intervals by using a first interpolation processing mode to obtain uniform time domain signal data; setting starting and ending frequencies and sampling starting and ending time for the uniform time domain signal data, and intercepting the data to obtain preprocessed time domain data; and processing the preprocessed time domain data by using a first data processing mode, and performing time-frequency conversion on the processed time domain data to obtain frequency domain data. According to the method, spline interpolation is carried out on the non-uniform time data, the uniform time data are rapidly acquired for sampling, the sampling technology of time-frequency conversion is enriched, and the problem that the conversion effect of converting the time domain to the frequency domain of the radio frequency microwave non-uniform time interval data is poor is solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of radio frequency and microwave, and specifically, the present invention relates to a spectrum analysis sampling method and a storage medium based on Gauss-Seidel iteration. Background Art

[0002] The method of converting time domain to frequency domain is crucial in aspects such as spectrum analysis, noise analysis, and filter design. Currently, common time-to-frequency sampling techniques include Fourier transform, etc. However, the existing methods have very poor conversion effects on data with non-uniform time intervals, and there is a lack of an efficient iterative interpolation method to fit non-uniform time data to obtain approximately real uniform time data. Summary of the Invention

[0003] To solve the above problems, the present invention proposes a spectrum analysis sampling method and a storage medium based on Gauss-Seidel iteration. Based on the spline interpolation method of Gauss-Seidel iteration, non-uniform time data is subjected to spline interpolation to quickly obtain uniform time data for sampling, enriching the sampling technology of time-frequency conversion, and solving the problem of poor conversion effect of converting time domain to frequency domain for data with non-uniform time intervals in radio frequency and microwave.

[0004] In the first aspect of the present invention, a spectrum analysis sampling method based on Gauss-Seidel iteration is provided, including:

[0005] S1: Obtain radio frequency and microwave time domain signal data, and determine whether the time interval of the time domain signal data is uniform. If it is uniform, execute step S3; if it is not uniform, execute step S2;

[0006] S2: For the time domain signal data with non-uniform time intervals, use the first interpolation processing mode to process the data to obtain uniform time domain signal data;

[0007] S3: Set the start and end frequencies and the start and end sampling times for the uniform time domain signal data to intercept the data and obtain preprocessed time domain data;

[0008] S4: Use the first data processing mode to process the preprocessed time domain data, and perform time-frequency conversion on the processed time domain data to obtain frequency domain data.

[0009] Further, in step S4, change the use of the first data processing mode to using the second data processing mode or the third data processing mode to process the preprocessed time domain data, and perform time-frequency conversion on the processed time domain data to obtain frequency domain data.

[0010] Further, in step S2, the data processing using the first interpolation processing mode includes: selecting one of the linear interpolation, quadratic spline interpolation, or cubic spline interpolation methods to resample the time-domain signal data with uneven time intervals into time-domain signal data with uniform time intervals.

[0011] Further, in step S3, for the uniform time-domain signal data X, set the sampling start time t start and the sampling end time t stop Intercept the time-domain signal data X. The intercepted time data is x[n], and the corresponding amplitude data is y[n], where 0 ≤ n < N, n is the sequence, N is the number of sampling points, the sampling interval is Δt, and set the start and end frequency ranges to f start ~f stop , the number of frequency points is numFreq, numFreq = (f stop -f start ) × (t stop -t start ) + 1, and the frequency interval is f step =(f stop -f start ) / (numFreq - 1).

[0012] Further, the first data processing mode includes: using the second interpolation processing mode to process the preprocessed time-domain data, and using the Gauss-Seidel iteration method to accelerate the solution of the tridiagonal matrix system in the second interpolation processing mode.

[0013] Further, the second interpolation processing mode includes:

[0014] S411, determine the minimum length L value and k value that satisfy L > N + numFreq - 1, such that L = 2 k ;

[0015] where L is the expected time-domain data length, N is the current time-domain data length, numFreq is the number of frequency points, and k is the exponential value of 2;

[0016] S412, select one of the linear interpolation, quadratic spline interpolation, or cubic spline interpolation methods to amplify and interpolate the preprocessed time-domain data to 2 k length.

[0017] Further, the second data processing mode includes: based on the discrete Fourier transform, fine-tuning and optimizing the integral formula through the midpoint rectangle method to achieve time-frequency conversion:

[0018]

[0019] k(f) = 1 - 2.0996·(f·Δt)2

[0020]

[0021] Wherein: X i is the discrete Fourier calculation result optimized by the midpoint rectangle method for the i-th one, where i is a non-negative integer; x[n] is the amplitude value of the n-th sampling point of the time-domain signal within the intercepted time interval; Δt is the sampling interval of the original signal, which determines the upper limit of the frequency for spectrum analysis; N is the current time-domain data length; f is the frequency value currently calculated; t start is the starting time of signal interception, which is used to locate the actual analysis time window; k(f) is the frequency weight correction factor, which suppresses the high-frequency integration error through a quadratic term and optimizes the amplitude approximation accuracy of the midpoint rectangle method; ω(f) is the phase correction term, which is used to compensate for the phase shift of the non-uniform sampling interval and improve the spectrum resolution.

[0022] Further, the specific third data processing mode includes:

[0023] S431, determine the minimum length L value and k value that satisfy L > N + numFreq - 1, such that L = 2 k ;

[0024] wherein, L is the expected time-domain data length, N is the number of sampling points, numFreq is the number of frequency points, and k is the exponential value of 2;

[0025] S432, obtain g(n) and h(n):

[0026]

[0027] Wherein x[n] is the time data and n is the sequence;

[0028] S433, multiply the Fourier transforms of g(n) and h(n), and perform the inverse Fourier transform on the result:

[0029]

[0030] where FFT is the Fourier transform and IFFT is the inverse Fourier transform;

[0031] S434, according to the number of sampling points N, obtain the frequency-domain data at the frequency f i = f start + i * Δf wherein, X i is the frequency-domain data result value corresponding to the frequency f i , i is 0, 1, 2, 3... L - 1, and Δf is the frequency interval.

[0032] Furthermore, the first data processing mode further includes:

[0033] Fitting formula: S i (x) = a i + b i (x - x i ) + c i (x - x i ) 2 + d i (x - x i ) 3 ;

[0034] First derivative: S′ i (x) = b i + 2c i (x - x i ) + 3d i (x - x i ) 2 ;

[0035] Second derivative: S″ i (x) = 2c i + 6d i (x - x i ) ;

[0036] m i = S″ i (x i ) ;

[0037] h i = x - x i ;

[0038] Matrix system:

[0039] where x is the current time value, S i (x) is the fitted time-domain data of the current time value, a i , b i , c i , d i are the fitting formula coefficients, x i is the i-th time value, y i is the time-domain data corresponding to the i-th time value;

[0040] Solve the matrix system using the Gauss-Seidel iteration solution formula;

[0041] The Gauss-Seidel iteration solution formula is:

[0042]

[0043] Among them, iter is the number of iterations; set the number of iterations of the Gauss-Seidel iteration to the matrix dimension minus 1, and sequentially solve for m1, m2, m3, m4...;

[0044]

[0045] After the solution is completed, substitute m i into the fitting formula to solve for a i , b i , c i , d i coefficients, and finally obtain the interpolated time-domain data S i (x).

[0046] In a second aspect of the present invention, a processor-readable storage medium is proposed. The processor-readable storage medium stores a computer program, and when the processor executes the computer program, it implements the spectrum analysis sampling method based on Gauss-Seidel iteration as described in the first aspect of the present invention.

[0047] The advantages of the present invention compared with the prior art are as follows:

[0048] The method of the present invention can sample time-domain information in multiple ways, and at the same time uses an interpolation method based on Gauss-Seidel iteration, which improves the sampling effect for non-uniform time data. In terms of interpolation speed, it also has a significant improvement compared with the ordinary simple iterative spline interpolation method, and preferably solves the problem of poor conversion effect from time domain to frequency domain for radio frequency microwave data with non-uniform time intervals. Description of the Drawings

[0049] Figure 1 is a schematic diagram of the steps of a spectrum analysis sampling method based on Gauss-Seidel iteration provided by an embodiment of the present invention.

[0050] Figure 2 is the time-domain experimental data provided by an embodiment of the present invention.

[0051] Figure 3 is the spectrum analysis result from -5 GHz to 5 GHz provided by an embodiment of the present invention.

[0052] Figure 4 is the spectrum analysis result from 0 GHz to 5 GHz provided by an embodiment of the present invention. Detailed Embodiments

[0053] Next, the technical solutions in the embodiments of the present application will be clearly described in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art belong to the scope of protection of the present application.

[0054] The terms "first", "second", etc. in the description and claims of this application are used to distinguish similar objects, rather than to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged under appropriate circumstances, so that the embodiments of this application can be implemented in an order other than those illustrated or described herein, and the objects distinguished by "first", "second", etc. are generally of the same category, and do not limit the number of objects. For example, the first object can be one or more. In addition, "and / or" in the description and claims means at least one of the connected objects, and the character " / ", generally represents an "or" relationship between the related objects before and after.

[0055] Method embodiments

[0056] The present invention mainly solves the problem of poor conversion effect of converting radio frequency microwave non-uniform time interval data from time domain to frequency domain.

[0057] In the first aspect of the present invention, a spectrum analysis sampling method based on Gauss-Seidel iteration is provided. The schematic flow diagram is as shown in the appendix Figure 1 as follows, and specifically includes:

[0058] S1: Obtain radio frequency microwave time domain signal data, and determine whether the time interval of the time domain signal data is uniform. If it is uniform, execute step S3; if it is not uniform, execute step S2.

[0059] S2: For the time domain signal data with non-uniform time intervals, use the first interpolation processing mode to process the data to obtain uniform time domain signal data.

[0060] In step S2, the use of the first interpolation processing mode to process the data includes: selecting one of the linear interpolation, quadratic spline interpolation or cubic spline interpolation methods to resample the time domain signal data with non-uniform time intervals into time domain signal data with uniform time intervals.

[0061] S3: Set the start and end frequencies and the start and end sampling times for the uniform time domain signal data to intercept the data and obtain preprocessed time domain data.

[0062] In step S3, for the uniform time domain signal data X, set the sampling start time t start and the sampling end time t stop Intercept the time domain signal data X. The intercepted time data is x[n], and the corresponding amplitude data is y[n], 0 ≤ n < N, where n is the sequence and N is the number of sampling points. Generally, t start = 0, t start and t stop The unit is seconds. The sampling interval is Δt.

[0063] Set the start and end frequency ranges to f start ~f stop , and by default, take f start =0, f stop =1 / (2Δt), the number of frequency points is numFreq, and generally take numFreq=(f stop -f start )×(t stop -t start ) + 1, and the frequency interval is f step =(f stop -f start ) / (numFreq - 1).

[0064] S4: Process the preprocessed time-domain data using the first data processing mode, perform time-frequency conversion on the processed time-domain data, and obtain frequency-domain data. Or process the preprocessed time-domain data using the second data processing mode or the third data processing mode, perform time-frequency conversion on the processed time-domain data, and obtain frequency-domain data.

[0065] Step S4 specifically includes steps S41, S42, and S43.

[0066] S41, process the preprocessed time-domain data using the first data processing mode, perform time-frequency conversion on the processed time-domain data, and obtain frequency-domain data.

[0067] The first data processing mode includes: processing the preprocessed time-domain data using the second interpolation processing mode, and accelerating the solution of the tridiagonal matrix system in the second interpolation processing mode using the Gauss-Seidel iteration method.

[0068] Among them, the second interpolation processing mode includes:

[0069] S411, determine the minimum length L value and k value that satisfy L > N + numFreq - 1, and make L = 2 k ;

[0070] Among them, L is the expected time-domain data length, N is the current time-domain data length, numFreq is the number of frequency points, and k is the exponential value of 2.

[0071] S412, select one of the linear interpolation, quadratic spline interpolation, or cubic spline interpolation methods, and amplify and interpolate the preprocessed time-domain data to 2 k length.

[0072] The first data processing mode is a method optimized by the cooperation of two steps based on the interpolation step and the iterative solution step. Specifically, in the interpolation step, the second interpolation processing mode is used to process the preprocessed time-domain data; in the iterative solution step, the Gauss-Seidel iteration method is used to accelerate the solution for the tridiagonal matrix system in the interpolation step, and by instantaneously updating the iterative variables, fast convergence is achieved.

[0073] The advantage of the first data processing mode is that by interpolating and amplifying the preprocessed time-domain data to a length of 2 k , the strong dependence of traditional FFT on uniform sampling is solved. The time-domain data of spline interpolation can better fit complex actual situations. By using the Gauss-Seidel iteration method to quickly approximate the interpolation result, fast interpolation and time-frequency conversion processing are achieved. Among them, cubic spline interpolation can significantly improve the fitting ability for complex signals by constraining the function, the continuity of the first-order and second-order derivatives. The first data processing mode has significantly better processing effects on the preprocessed time-domain data of the original time-domain signal data with uneven time intervals than the second and third data processing modes.

[0074] Exemplarily, taking cubic spline interpolation as an example, the two-step cooperation and optimization process of the interpolation step and the iterative solution step are illustrated.

[0075] According to the principle of cubic spline fitting, three formulas for the fitting formula, the first derivative, and the second derivative are listed, which are respectively:

[0076] Fitting formula: S i (x) = a i + b i (x - x i ) + c i (x - x i ) 2 + d i (x - x i ) 3 ;

[0077] First derivative: S′ i (x) = b i + 2c i (x - x i ) + 3d i (x - x i ) 2 ;

[0078] Second derivative: S″ i (x) = 2c i + 6d i (x - x i ).

[0079] Simplify the second derivative, let:

[0080] m i = S″ i (x i )

[0081] h i = x - x i

[0082] Substituting it into the original fitting formula, a matrix system Ax = b is obtained:

[0083]

[0084] where x is the current time value, S i (x) is the fitting time-domain data of the current time value, a i , b i , c i , d i are the fitting formula coefficients, x i is the i-th time value, and y i is the time-domain data corresponding to the i-th time value.

[0085] The traditional iterative method uses LR decomposition and the iterative method to solve for m i , and then substitutes m i into the fitting formula to solve for a i , b i , c i , d i These coefficients, and finally use these coefficients to calculate the interpolation S i (x).

[0086] In this embodiment, in the iterative solution step of the first data processing mode, the Gauss-Seidel iterative solution formula is used to solve this matrix system.

[0087] The following is the Gauss-Seidel iterative solution formula:

[0088]

[0089] where iter is the number of iterations, and the other variables have the same meanings as above.

[0090] The Gauss-Seidel iterative solution formula converges faster than the iterative method of the traditional iterative method. The difference between it and the traditional iterative method lies in the calculation when it will use

[0091] Since the right side of the fitting formula can be converted into the form of the following formula, then only need to set the Gauss-Seidel iteration number to the matrix dimension - 1, and m1, m2, m3, m4... can be solved sequentially.

[0092]

[0093] After the solution is completed, substitute m i into the fitting formula to solve for a i , b i , c i , d i and other coefficients, and finally obtain the interpolated time-domain data S i (x).

[0094] Compared with linear interpolation, the time-domain data of spline interpolation can better fit complex actual situations.

[0095] For quadratic spline interpolation, the biggest difference from cubic spline interpolation is that the fitting formula is S i (x) = a i + b i (x - x i ) + c i (x - x i ) 2 .

[0096] Other solution methods are similar to those of cubic spline interpolation. The matrix system of quadratic spline interpolation can be solved by following the solution method of the above cubic spline interpolation, which will not be elaborated here.

[0097] S42, process the preprocessed time-domain data using the second data processing mode, and perform time-frequency conversion on the processed time-domain data to obtain frequency-domain data.

[0098] The second data processing mode specifically includes: based on the traditional discrete Fourier transform (DFT), fine-tune and optimize the integral formula through the midpoint rectangle method to achieve time-frequency conversion:

[0099]

[0100] k(f) = 1 - 2.0996·(f·Δt) 2

[0101]

[0102] where:

[0103] X i is the discrete Fourier calculation result optimized by the midpoint rectangle method for the i-th one, and i is a non-negative integer.

[0104] x[n] is the amplitude value of the n-th sampling point of the time-domain signal within the intercepted time interval.

[0105] Δt is the sampling interval of the original signal, which determines the upper frequency limit of the spectrum analysis.

[0106] N is the current time-domain data length.

[0107] f is the currently calculated frequency value.

[0108] t start is the starting time of signal interception, used to locate the time window for actual analysis.

[0109] k(f) is the frequency weight correction factor, which suppresses the high-frequency integration error through quadratic terms and optimizes the amplitude approximation accuracy of the midpoint rectangle method.

[0110] ω(f) is the phase correction term, used to compensate for the phase shift of non-uniform sampling intervals and improve the spectral resolution.

[0111] The advantage of adopting the second data processing mode is as follows: Based on the traditional discrete Fourier transform (DFT), the second data processing mode realizes time-frequency conversion by fine-tuning and optimizing the integral formula through the midpoint rectangle method. The rectangular integral of the original DFT assumes that the signal is constant within the sampling interval, resulting in the accumulation of high-frequency component errors. The second data processing mode introduces the frequency weight factor k(f) and the phase correction term ω(f) to correct the amplitude and phase respectively, solves the problem of cumulative errors of the traditional DFT rectangular integration method in the high-frequency band, takes into account both computational efficiency and accuracy, approximates the midpoint value instead of the interval integral, and effectively suppresses high-frequency oscillation errors. While maintaining the original computational complexity, the second data processing mode improves the ability to suppress spectral leakage, especially suitable for scenarios that require both efficiency and accuracy in wide-frequency domain analysis, and overall improves the frequency domain resolution and computational accuracy.

[0112] S43. Process the preprocessed time-domain data using the third data processing mode, perform time-frequency conversion on the processed time-domain data, and obtain frequency-domain data.

[0113] The third data processing mode specifically includes:

[0114] S431. Determine the minimum length L value and k value that satisfy L > N + numFreq - 1, such that L = 2 k ;

[0115] where L is the expected time-domain data length, N is the current time-domain data length, numFreq is the number of frequency points, and k is the exponential value of 2.

[0116] S432. Obtain g(n) and h(n):

[0117]

[0118] where x[n] is the time data and n is the sequence.

[0119] S433. Multiply the Fourier transforms of g(n) and h(n), and perform the inverse Fourier transform on the result (i.e., implement convolution through FFT):

[0120]

[0121] where FFT is the Fourier transform and IFFT is the inverse Fourier transform.

[0122] S434. Obtain the frequency-domain data at a frequency of f i = f start + i*Δf,

[0123] where X i is the result value of the frequency-domain data corresponding to the frequency f i , i is 0, 1, 2, 3…L - 1, W is the same as above, and Δf is the frequency interval.

[0124] The advantage of adopting the third data processing mode is as follows: The existing Chirp-Z algorithm directly performs sparse and uniform sampling on the target frequency band by parameterizing the starting point and step size of the frequency band. The third data processing mode optimizes the operation efficiency of the existing Chirp-Z algorithm in engineering implementation, accelerates the convolution operation in the Chrip-Z algorithm with the help of FFT, reduces its computational complexity, makes the third data processing mode significantly superior to the computational complexity of directly performing convolution, and solves the problem of efficient calculation for narrowband spectrum analysis.

[0125] Furthermore, the second and third data processing modes also use interpolation for non-uniform time data, and the spline interpolation method is selected to interpolate the time-domain data, using the Gauss-Seidel iteration described in the first data processing mode.

[0126] Exemplarily, open the iViewer tool in the AetherMW tool, import a set of time-domain data data, and a segment of the time-domain data used is as shown in the appendix Figure 2 . Enter the expression freqRes = fs(data) in the expression. Where freqRes is the converted frequency-domain result, and fs is the time-frequency conversion function constructed based on the foregoing method. The effect diagram of freqRes after drawing in the iViewer tool is as shown in the appendix Figure 3 to the appendix Figure 4 . Where the abscissa is the frequency and the ordinate is the amplitude.

[0127] In a second aspect, the present invention proposes a processor-readable storage medium, on which a computer program is stored, and the computer program can be loaded and executed by a processor to implement the spectrum analysis sampling method based on Gauss-Seidel iteration described in the first aspect.

[0128] The embodiments of the present application have been described above in conjunction with the accompanying drawings. However, the present application is not limited to the above specific embodiments. The above specific embodiments are merely illustrative and not restrictive. Under the inspiration of the present application, those of ordinary skill in the art can also make many forms without departing from the purpose of the present application and the scope protected by the claims, and all of them fall within the protection scope of the present application.

Claims

1. A spectrum analysis sampling method based on Gauss-Seidel iteration, characterized in that, Including: S1: Obtain radio frequency microwave time-domain signal data, and determine whether the time interval of the time-domain signal data is uniform. If it is uniform, execute step S3; if it is not uniform, execute step S2. S2: For the time-domain signal data with non-uniform time intervals, use the first interpolation processing mode to process the data to obtain uniform time-domain signal data. S3: Set the start and end frequencies and the start and end sampling times for the uniform time-domain signal data to intercept the data and obtain preprocessed time-domain data. S4: Use the first data processing mode to process the preprocessed time-domain data, and perform time-frequency conversion on the processed time-domain data to obtain frequency-domain data.

2. The spectrum analysis sampling method based on Gauss-Seidel iteration according to claim 1, characterized in that: In step S4, change the use of the first data processing mode to using the second data processing mode or the third data processing mode to process the preprocessed time-domain data, and perform time-frequency conversion on the processed time-domain data to obtain frequency-domain data.

3. The spectrum analysis sampling method based on Gauss-Seidel iteration according to claim 1, characterized in that: In step S2, the use of the first interpolation processing mode to process the data includes: selecting one of the linear interpolation, quadratic spline interpolation, or cubic spline interpolation methods to resample the time-domain signal data with non-uniform time intervals into time-domain signal data with uniform time intervals.

4. The spectrum analysis sampling method based on Gauss-Seidel iteration according to claim 1, characterized in that: In step S3, for the uniform time-domain signal data X, set the sampling start time t start and the sampling end time t stop Intercept the time-domain signal data X. The intercepted time data is x[n], and the corresponding amplitude data is y[n], where 0 ≤ n < N, n is the sequence, N is the number of sampling points, the sampling interval is Δt, and the start and end frequency ranges are set as f start ~f stop , the number of frequency points is numFreq, numFreq = (f stop -f start ) × (t stop -t start ) + 1, and the frequency interval is f step =(f stop -f start ) / (numFreq - 1).

5. The spectrum analysis sampling method based on Gauss-Seidel iteration according to claim 1, characterized in that: The first data processing mode includes: using the second interpolation processing mode to process the preprocessed time-domain data, and using the Gauss-Seidel iteration method to accelerate the solution of the tridiagonal matrix system in the second interpolation processing mode.

6. The spectrum analysis sampling method based on Gauss-Seidel iteration according to claim 5, characterized in that: The second interpolation processing mode includes: S411, determine the minimum length L value and k value that satisfy L > N + numFreq - 1, and make L = 2 k ; where L is the expected time-domain data length, N is the current time-domain data length, numFreq is the number of frequency points, and k is the exponential value of 2; S412, select one of the linear interpolation, quadratic spline interpolation or cubic spline interpolation methods, and amplify and interpolate the preprocessed time-domain data to 2 k lengths.

7. The spectrum analysis sampling method based on Gauss-Seidel iteration according to claim 2, characterized in that: The second data processing mode includes: on the basis of the discrete Fourier transform, fine-tuning and optimizing the integral formula through the midpoint rectangle method to achieve time-frequency conversion: k(f) = 1 - 2.0996·(f·Δt) 2 Where: X i is the discrete Fourier calculation result optimized by the midpoint rectangle method for the i-th one, where i is a non-negative integer; x[n] is the amplitude value of the n-th sampling point of the time-domain signal within the intercepted time interval; Δt is the sampling interval of the original signal, which determines the upper frequency limit of the spectrum analysis; N is the current time-domain data length; f is the currently calculated frequency value; t start is the start time of the signal interception, which is used to locate the actual analysis time window; k(f) is the frequency weight correction factor, which suppresses the high-frequency integration error through the quadratic term and optimizes the amplitude approximation accuracy of the midpoint rectangle method; ω(f) is the phase correction term, which is used to compensate for the phase shift of the non-uniform sampling interval and improve the spectrum resolution.

8. A spectrum analysis sampling method based on Gauss-Seidel iteration according to claim 2, characterized in that, The third data processing mode specifically includes: S431, determine the minimum length L value and k value that satisfy L > N + numFreq - 1, and make L = 2 k ; where L is the expected time-domain data length, N is the number of sampling points, numFreq is the number of frequency points, and k is the exponential value of 2; S432, obtain g(n) and h(n): wherein x[n] is time data, and n is a sequence; S433, multiply the Fourier transforms of g(n) and h(n), and perform the inverse Fourier transform on the result: where FFT is the Fourier transform and IFFT is the inverse Fourier transform; S434, obtain the frequency f according to the number of sampling points N i = f start + i * Δf, where i is 0, 1, 2, 3... L - 1, and Δf is the frequency interval where X i is the result value of the frequency domain data corresponding to the frequency f i i is 0, 1, 2, 3…L - 1, and Δf is the frequency interval 9. A spectrum analysis sampling method based on Gauss-Seidel iteration according to claim 6, characterized in that, The first data processing mode further includes: Fitting formula: S i (x) = a i + b i (x - x i ) + c i (x - x i ) 2 + d i (x - x i ) 3 ; First derivative: S′ i (x) = b i + 2c i (x - x i ) + 3d i (x - x i ) 2 ; Second derivative: S″ i (x) = 2c i + 6d i (x - x i ); m i = S″ i (x i ); h i = x - x i ; Matrix system: where x is the current time value, S i (x) is the fitted time-domain data of the current time value, a i , b i , c i , d i are the coefficients of the fitting formula, x i is the i-th time value, y i is the time-domain data corresponding to the i-th time value; Using the Gauss-Seidel iteration solution formula to solve the matrix system; The Gauss-Seidel iteration solution formula is: Among them, iter is the number of iterations; set the number of iterations of the Gauss-Seidel iteration to the matrix dimension minus 1, and sequentially solve m1, m2, m3, m4...; After the solution is completed, substitute m i into the fitting formula to solve for a i , b i , c i , d i coefficients, and finally obtain the interpolated time-domain data S i (x).

10. A processor-readable storage medium, characterized in that, The processor-readable storage medium stores a computer program, and when the processor executes the computer program, it implements the spectrum analysis sampling method based on Gauss-Seidel iteration according to any one of claims 1 to 9.

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