A fourier transform signal calibration method and system fusing robust regression

Abstract

The application discloses a Fourier transform signal calibration method and system fusing robust regression, and belongs to the technical field of signal processing; the method comprises inputting an original signal; the original signal is a signal containing low SNR noise; SNR-driven adaptive pretreatment is performed on the original signal; DFT preliminary parameter estimation is performed on the pretreated signal; the Huber robust regression model is used to correct the preliminary phase estimation value; spectrum smoothing and parabolic interpolation are combined to break through the limitation of traditional Fourier transform frequency resolution; and the optimized phase, frequency and amplitude estimation values are integrated to output accurate signal parameters; the problems of spectrum leakage and fence effect of traditional Fourier transform in the prior art under a low signal-to-noise ratio environment are solved, and accurate estimation of signal frequency, phase and amplitude is realized.

Description

Technical Field

[0001] This invention relates to the field of signal processing technology, and in particular to a method and system for calibrating Fourier transform signals that incorporates robust regression. Background Technology

[0002] In practical engineering fields such as communications, sensor applications, and geological exploration, the frequency, phase, and amplitude of a signal are core indicators for evaluating system performance. Their estimation accuracy directly determines the precision of equipment control, the quality of data processing, and the reliability of measurement results. In geological exploration systems, accurate estimation of signal phase and frequency is crucial for signal demodulation, thereby enabling precise detection of underground resources.

[0003] In real-world engineering scenarios, signals are susceptible to interference from multiple factors: on the one hand, the frequency error, drift, and phase noise of the crystal oscillator itself can cause inherent deviations in signal transmission and processing; on the other hand, external environmental interference can significantly reduce the signal-to-noise ratio (SNR), especially under complex operating conditions, where the SNR may drop below -15dB, posing a significant challenge to signal parameter estimation. Fourier transform is a classic method for signal parameter estimation. However, it faces inherent technical bottlenecks in low SNR environments: firstly, spectral leakage, due to the discreteness and finiteness of signal sampling, making it impossible to accurately match signal frequencies that are not integer multiples of the sampling frequency, leading to spectral energy diffusion; secondly, the picket fence effect, which can only obtain spectral values ​​at discrete frequency points and cannot capture continuous spectral characteristics. These two problems directly result in a significant reduction in the estimation accuracy of frequency, phase, and amplitude under low SNR, making it difficult to meet practical engineering needs. Summary of the Invention

[0004] This invention provides a Fourier transform signal calibration method and system that integrates robust regression to solve the problems of spectral leakage and picket fence effect in traditional Fourier transform under low signal-to-noise ratio environments, and to achieve accurate estimation of signal frequency, phase and amplitude.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] This invention provides a Fourier transform signal calibration method incorporating robust regression, comprising:

[0007] S1: Input the original signal, which is a signal containing low SNR noise;

[0008] S2: Perform SNR-driven adaptive preprocessing on the original signal;

[0009] S3: Perform preliminary DFT parameter estimation on the preprocessed signal;

[0010] S4: Correcting the initial phase estimate based on the Huber robust regression model;

[0011] S5: Combining spectral smoothing and parabolic interpolation, it breaks through the frequency resolution limitations of traditional Fourier transform;

[0012] S6: Integrates and optimizes the phase, frequency, and amplitude estimates to output accurate signal parameters.

[0013] Furthermore, the original signal type is: s(t) = Asin(2πft + )+n(t);

[0014] Where: A is the signal amplitude;

[0015] f is the signal frequency, ranging from 2 to 100 kHz;

[0016] For signal phase;

[0017] n(t) is Gaussian white noise that is uncorrelated with the signal.

[0018] Furthermore, S2 includes:

[0019] S21: Signal windowing and segmented overlap processing: The Hanning window function is used to suppress spectral leakage, and the original signal is divided into M overlapping data segments; wherein, the original signal is: x(n) = s(n) + w(n),

[0020] in:

[0021] n = 0, 1, ..., N-1, where N and n are the number of sampling points in a single run;

[0022] s(n) is the pure target signal;

[0023] w(n) is Gaussian white noise;

[0024] S22: Power spectral density calculation: Perform Discrete Fourier Transform (DFT) on each overlapping signal segment to calculate the power spectral density at each frequency point:

[0025] S23: Signal and noise frequency band segmentation: Distinguish between signal and noise frequency bands based on differences in power spectrum distribution;

[0026] S24: SNR estimation: Calculate the average power ratio of the two frequency bands to obtain the SNR: a dynamic adjustment parameter;

[0027] S25: Extraction of mixing and difference frequency signals.

[0028] Furthermore, S4 includes:

[0029] S41: Construction of regression sample set: The time series X=[0,1 / Ts,...,(N-1) / Ts], where Ts is the sampling period or frequency point, is used as the input feature, and the preliminary phase estimate is used as the output sample;

[0030] S42: Huber loss function definition: balancing estimation efficiency and robustness against outliers;

[0031]

[0032] For residuals;

[0033] S43: Solving for optimal parameters: Minimize the objective function using gradient descent, as shown in the following formula:

[0034]

[0035] in:

[0036] The derivative of the loss function Huber;

[0037] The expanded input feature vector;

[0038] S44: Compensated Phase Output: Substitute the input sample into the trained model to obtain the compensated phase.

[0039] Furthermore, S5 includes:

[0040] S51: Spectral smoothing: Perform moving average smoothing on the DFT spectrum to reduce random fluctuations in the spectrum under low SNR and preserve peak characteristics;

[0041] S52: Feature point localization: Locate the peak point k of the smoothed spectrum and its left and right adjacent points k-1 and k+1, and record the frequency [f(k-1), f(k), f(k+1)] and the corresponding amplitude [A(k-1), A(k), A(k+1)] of the three points;

[0042] S53: Quadratic polynomial fitting: Construct a parabolic interpolation model A(f)=af2+bf+c, substitute the coordinates of the three points, and obtain the coefficients a, b, and c by solving the system of equations;

[0043] S54: Frequency Refinement Calculation: Differentiate the polynomial and set the derivative to zero to obtain an accurate frequency estimate.

[0044] This invention also provides a Fourier transform signal calibration system that integrates robust regression, comprising:

[0045] Input module: used to input the raw signal, which is a signal containing SNR noise;

[0046] Preprocessing module: used to perform SNR-driven adaptive preprocessing on the original signal;

[0047] Parameter estimation module: used to perform preliminary DFT parameter estimation on the preprocessed signal;

[0048] Correction module: Used to correct the initial phase estimate based on the Huber robust regression model;

[0049] Smoothing interpolation module: Used to combine spectral smoothing and parabolic interpolation to break through the frequency resolution limitations of traditional Fourier transform;

[0050] Output module: Used to integrate the optimized phase, frequency and amplitude estimates and output accurate signal parameters.

[0051] Compared with the prior art, the technical solution disclosed in this invention has the following beneficial effects:

[0052] This invention incorporates SNR adaptive adjustment on the basis of robust regression compensation. It achieves the transformation from low signal-to-noise ratio to high signal-to-noise ratio by using Fourier analysis, robust regression compensation, and parabolic interpolation refinement. It can realize high-precision calculation of signal frequency, phase, and amplitude in low signal-to-noise ratio (-10dB to -15dB) environments, meeting the requirements of fields such as sensors. Attached Figure Description

[0053] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0054] Figure 1 A schematic diagram of the Fourier transform signal calibration method based on robust regression provided in this embodiment of the invention. Detailed Implementation

[0055] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0056] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0057] This invention provides a Fourier transform signal calibration method and system that integrates robust regression to solve the problems of spectral leakage and picket fence effect in traditional Fourier transform under low signal-to-noise ratio environments, and to achieve accurate estimation of signal frequency, phase and amplitude.

[0058] This invention provides a method for calibrating Fourier transform signals based on robust regression, comprising:

[0059] S1: Input the original signal, which contains low SNR noise (-10dB to -15dB).

[0060] In this embodiment of the invention, raw signals are received from communication equipment, sensors, geological exploration systems, and other scenarios. The signal type is a sinusoidal signal, adapted to common engineering scenarios. The raw signal type is: s(t) = Asin(2πft + )+n(t);

[0061] Where: A is the signal amplitude (parameter to be estimated);

[0062] f is the signal frequency (a parameter to be estimated, ranging from 2 to 100 kHz).

[0063] The signal phase (parameter to be estimated);

[0064] n(t) is Gaussian white noise that is uncorrelated with the signal.

[0065] S2: Perform SNR-driven adaptive preprocessing on the original signal.

[0066] In this embodiment of the invention, the SNR of the input noisy signal is detected in real time, and the acquisition parameters (sampling frequency, number of sampling points) and filtering parameters (filter type, cutoff frequency) are dynamically adjusted according to the SNR. At the same time, the high-frequency signal is converted into a low-frequency difference frequency signal through mixing to filter out strong noise.

[0067] S3: Perform preliminary parameter estimation using DFT on the preprocessed signal.

[0068] In this embodiment of the invention, the preprocessed signal is subjected to preliminary DFT parameter estimation to obtain preliminary frequency, phase and amplitude estimates, providing basic data for subsequent precise optimization.

[0069] S4: The initial phase estimate is corrected based on the Huber robust regression model to suppress noise outliers and improve the robustness of the phase estimate.

[0070] S5: Combining spectral smoothing and parabolic interpolation, it breaks through the frequency resolution limitation of traditional Fourier transform to improve frequency estimation accuracy.

[0071] S6: Integrates and optimizes the phase, frequency, and amplitude estimates to output accurate signal parameters.

[0072] Furthermore, S2 includes:

[0073] S21: Signal windowing and segmented overlap processing: The Hanning window function is used to suppress spectral leakage, and the original signal is divided into M overlapping segments; where the original signal is: x(n) = s(n) + w(n),

[0074] in:

[0075] n = 0, 1, ..., N-1, where N and n are the number of sampling points in a single run;

[0076] s(n) is the pure target signal;

[0077] w(n) is Gaussian white noise;

[0078] S22: Power spectral density calculation: Perform Discrete Fourier Transform (DFT) on each overlapping signal segment to calculate the power spectral density at each frequency point:

[0079] S23: Signal and noise frequency band segmentation: Based on the difference in power spectrum distribution, distinguish between the signal frequency band (high power concentrated area) and the noise frequency band (low power dispersed area).

[0080] S24: SNR Estimation: Calculate the average power ratio of the two frequency bands to obtain the SNR: a dynamically adjusted parameter;

[0081] S25: Mixing and difference frequency signal extraction (high frequency signal adaptation).

[0082] Furthermore, S4 includes:

[0083] S41: Construction of regression sample set: The time series X=[0,1 / Ts,...,(N-1) / Ts], where Ts is the sampling period or frequency point, is used as the input feature, and the preliminary phase estimate is used as the output sample;

[0084] S42: Huber loss function definition: balancing estimation efficiency and robustness against outliers;

[0085]

[0086] For residuals;

[0087] S43: Solving for optimal parameters: Minimize the objective function using gradient descent, as shown in the following formula:

[0088]

[0089] in:

[0090] The derivative of Huber's loss function;

[0091] Expanded input feature vector;

[0092] S44: Compensated Phase Output: Substitute the input sample into the trained model to obtain the compensated phase.

[0093] Furthermore, S5 includes:

[0094] S51: Spectral smoothing: Perform moving average smoothing on the DFT spectrum to reduce random fluctuations in the spectrum under low SNR and preserve peak characteristics;

[0095] S52: Feature point localization: Locate the peak point k of the smoothed spectrum and its left and right adjacent points k-1 and k+1, and record the frequency [f(k-1), f(k), f(k+1)] and the corresponding amplitude [A(k-1), A(k), A(k+1)] of the three points;

[0096] S53: Quadratic polynomial fitting: Construct a parabolic interpolation model A(f)=af2+bf+c, substitute the coordinates of the three points, and obtain the coefficients a, b, and c by solving the system of equations;

[0097] S54: Frequency Refinement Calculation: By differentiating the polynomial and setting the derivative to zero, an accurate frequency estimate is obtained. The frequency estimation error is ≤0.025Hz at low SNR=-10dB, which is more than 60% lower than the error of traditional FFT.

[0098] This invention also provides a Fourier transform signal calibration system that integrates robust regression, comprising:

[0099] Input module: Used to input the raw signal, which is a signal containing SNR noise;

[0100] Preprocessing module: Used for SNR-driven adaptive preprocessing of the original signal;

[0101] Parameter estimation module: used to perform preliminary DFT parameter estimation on the preprocessed signal;

[0102] Correction module: Used to correct the initial phase estimate based on the Huber robust regression model;

[0103] Smoothing interpolation module: Used to combine spectral smoothing and parabolic interpolation to break through the frequency resolution limitations of traditional Fourier transform;

[0104] Output module: Used to integrate the optimized phase, frequency and amplitude estimates and output accurate signal parameters.

[0105] The basic principles of the present invention have been described above with reference to specific embodiments. However, it should be noted that the advantages, benefits, and effects mentioned in the present invention are merely examples and not limitations, and should not be considered as essential features of each embodiment of the present invention. Furthermore, the specific details disclosed above are for illustrative and facilitative purposes only, and are not limitations. These details do not limit the present invention to the necessity of employing the aforementioned specific details.

[0106] The block diagrams of devices, apparatuses, devices, and systems involved in this invention are merely illustrative examples and are not intended to require or imply that they must be connected, arranged, or configured in the manner shown in the block diagrams. As those skilled in the art will recognize, these devices, apparatuses, devices, and systems can be connected, arranged, and configured in any manner. Words such as “comprising,” “including,” “having,” etc., are open-ended terms meaning “including but not limited to,” and are used interchangeably with them. The terms “or” and “and” as used herein refer to the terms “and / or,” and are used interchangeably with them unless the context clearly indicates otherwise. The term “such as” as used herein refers to the phrase “such as but not limited to,” and is used interchangeably with it.

[0107] It should also be noted that in the apparatus, device, and method of the present invention, the components or steps can be disassembled and / or recombined. These disassemblies and / or recombinations should be considered as equivalent solutions of the present invention.

[0108] The above description of the disclosed aspects is provided to enable any person skilled in the art to make or use the invention. Various modifications to these aspects will be readily apparent to those skilled in the art, and the general principles defined herein can be applied to other aspects without departing from the scope of the invention. Therefore, the invention is not intended to be limited to the aspects shown herein, but rather to be carried out within the widest scope consistent with the principles and novel features disclosed herein.

[0109] It should be understood that the qualifying terms "first", "second", "third", "fourth", "fifth" and "sixth" used in the description of the embodiments of the present invention are only used to more clearly illustrate the technical solutions and are not intended to limit the scope of protection of the present invention.

[0110] The above description has been given for purposes of illustration and description. Furthermore, this description is not intended to limit the embodiments of the invention to the forms disclosed herein. Although numerous exemplary aspects and embodiments have been discussed above, those skilled in the art will recognize certain variations, modifications, alterations, additions, and sub-combinations therein.

Claims

1. A Fourier transform signal calibration method incorporating robust regression, characterized in that, include: S1: Input the original signal, which is a signal containing low SNR noise; S2: Perform SNR-driven adaptive preprocessing on the original signal; S3: Perform preliminary DFT parameter estimation on the preprocessed signal; S4: Correcting the initial phase estimate based on the Huber robust regression model; S5: Combining spectral smoothing and parabolic interpolation, it breaks through the frequency resolution limitations of traditional Fourier transform; S6: Integrates and optimizes the phase, frequency, and amplitude estimates to output accurate signal parameters.

2. The Fourier transform signal calibration method based on robust regression as described in claim 1, characterized in that, The original signal type is: s(t) = Asin(2πft + ... )+n(t); Where: A is the signal amplitude; f is the signal frequency, ranging from 2 to 100 kHz; For signal phase; n(t) is Gaussian white noise that is uncorrelated with the signal.

3. The Fourier transform signal calibration method based on robust regression as described in claim 1, characterized in that, The S2 includes: S21: Signal windowing and segmented overlap processing: The Hanning window function is used to suppress spectral leakage, and the original signal is divided into M overlapping data segments; wherein, the original signal is: x(n) = s(n) + w(n), in: n = 0, 1, ..., N-1, where N and n are the number of sampling points in a single run; x(n) is the original signal; s(n) is the pure target signal; w(n) is Gaussian white noise; S22: Power spectral density calculation: Perform Discrete Fourier Transform (DFT) on each overlapping signal segment to calculate the power spectral density at each frequency point: S23: Signal and noise frequency band segmentation: Distinguish between signal and noise frequency bands based on differences in power spectrum distribution; S24: SNR estimation: Calculate the average power ratio of the two frequency bands to obtain the SNR; dynamically adjust parameters; S25: Extraction of mixing and difference frequency signals.

4. The Fourier transform signal calibration method based on robust regression as described in claim 1, characterized in that, S4 includes: S41: Construction of regression sample set: The time series X=[0,1 / Ts,...,(N-1) / Ts], where Ts is the sampling period or frequency point, is used as the input feature, and the preliminary phase estimate is used as the output sample; S42: Huber loss function definition: balancing estimation efficiency and outlier resistance; The residuals of the regression model; The threshold parameter for Huber loss; For the squared residuals; As a linear term, when the residual is greater than the threshold, the loss increases linearly with the absolute value of the residual, thus avoiding excessive penalty to the model by large residuals. This is a constant correction term to ensure the function is in... The function is continuously differentiable at a given point, which allows for a smooth transition of the entire Huber loss function. S43: Solving for optimal parameters: Minimize the objective function using gradient descent, as shown in the following formula: in: Let be the objective function to be minimized; This represents the vector of parameters to be optimized in the regression model. The sample index ranges from 0 to M-1; The derivative of the loss function Huber; Let be the residual of the i-th sample; The expanded input feature vector; S44: Compensated Phase Output: Substitute the input sample into the trained model to obtain the compensated phase.

5. The Fourier transform signal calibration method based on robust regression as described in claim 1, characterized in that, S5 includes: S51: Spectral smoothing: Perform moving average smoothing on the DFT spectrum to reduce random fluctuations in the spectrum under low SNR and preserve peak characteristics; S52: Feature point localization: Locate the peak point k of the smoothed spectrum and its left and right adjacent points k-1 and k+1, and record the frequency [f(k-1), f(k), f(k+1)] and the corresponding amplitude [A(k-1), A(k), A(k+1)] of the three points; S53: Quadratic Polynomial Fitting: Constructing a Parabolic Interpolation Model Substitute the coordinates of the three points into the equations and solve the system of equations to obtain the coefficients a, b, and c. S54: Frequency Refinement Calculation: Differentiate the polynomial and set the derivative to zero to obtain an accurate frequency estimate.

6. A Fourier transform signal calibration system incorporating robust regression, characterized in that, include: Input module: used to input the raw signal, which is a signal containing SNR noise; Preprocessing module: used to perform SNR-driven adaptive preprocessing on the original signal; Parameter estimation module: used to perform preliminary DFT parameter estimation on the preprocessed signal; Correction module: Used to correct the initial phase estimate based on the Huber robust regression model; Smoothing interpolation module: Used to combine spectral smoothing and parabolic interpolation to break through the frequency resolution limitations of traditional Fourier transform; Output module: Used to integrate the optimized phase, frequency and amplitude estimates and output accurate signal parameters.

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