Time-frequency signal processing method and device based on CEEMDAN

Abstract

The application relates to the technical field of data processing, in particular to a time-frequency signal processing method and device based on CEEMDAN. The method comprises the following steps: performing ensemble average empirical mode decomposition on a to-be-processed time-frequency signal through CEEMDAN to obtain a plurality of initial intrinsic mode functions; performing time-frequency analysis on the plurality of initial intrinsic mode functions to generate signal analysis parameters of the to-be-processed time-frequency signal; obtaining a plurality of final intrinsic mode functions meeting certain conditions based on the signal analysis parameters and the plurality of initial intrinsic mode functions; performing information fusion on the plurality of final intrinsic mode functions to obtain fused intrinsic mode functions, and then processing the to-be-processed time-frequency signal to obtain a processed time-frequency signal. Thus, the problems that in the related art, the processing of nonlinear and non-stationary signals is not real-time and effective, cannot be applied to the processing of large-scale data sets, the application range is narrow in actual processing, and the actual requirements of signal processing and analysis cannot be met are solved.

Description

Technical Field

[0001] This application relates to the field of data processing technology, and in particular to a time-frequency signal processing method and apparatus based on CEEMDAN. Background Technology

[0002] Time-frequency signals refer to the characteristics of a signal in both the time domain and the frequency domain. In signal processing, we frequently use the concepts of time domain and frequency domain to describe the properties of a signal. In practical applications, time-frequency signal analysis is commonly used in audio processing, communication systems, radar systems, timekeeping, time synchronization, satellite navigation, and other fields. Traditional signal processing methods have certain limitations in handling nonlinear and non-stationary signals; traditional methods such as Fourier transforms are insufficient when processing such complex signals.

[0003] In related technologies, adaptive signal decomposition of nonlinear and non-stationary signals can be performed through empirical mode decomposition. By decomposing a complex dataset into a series of intrinsic mode functions (EMFs), each EMF possesses symmetry, a local mean of zero, the same number of zero-crossing points and extrema, and the instantaneous frequency at any point is meaningful. This decomposition method allows each EMF to reflect a portion of the data's characteristics, facilitating in-depth analysis of complex signals. Alternatively, an improved version of CEEMDAN (Complete Ensemble Empirical Mode Decomposition with Adaptive Noise) can be used to decompose a preprocessed MI-EEG (Motor Imagery Electroencephalogram) dataset, obtaining a series of EMFs. Then, the sample entropy method and K-means clustering method are used to obtain EMFs with key information, thereby obtaining the time-frequency representation of the MI-EEG signal.

[0004] However, the related technologies are not real-time and effective enough for processing nonlinear and non-stationary signals, and cannot be applied to the processing of large-scale datasets. In practical processing, their application scope is narrow and cannot meet the actual needs of signal processing and analysis, so they urgently need to be improved. Summary of the Invention

[0005] This application provides a time-frequency signal processing method and apparatus based on CEEMDAN to solve the problems in related technologies, such as insufficient real-time and effectiveness in processing nonlinear and non-stationary signals, inability to process large-scale datasets, narrow application scope in practical processing, and inability to meet the actual needs of signal processing and analysis.

[0006] The first aspect of this application provides a time-frequency signal processing method based on CEEMDAN, comprising the following steps: performing ensemble-averaged empirical mode decomposition on the time-frequency signal to be processed using CEEMDAN to obtain multiple initial intrinsic mode functions (IMFs) of the time-frequency signal to be processed; performing time-frequency analysis on the multiple initial IMFs to generate signal analysis parameters of the time-frequency signal to be processed; obtaining multiple final IMFs that satisfy preset conditions from the multiple initial IMFs based on the signal analysis parameters and the multiple initial IMFs; performing information fusion on the multiple final IMFs to obtain fused IMFs; and processing the time-frequency signal to be processed based on the fused IMFs to obtain a processed time-frequency signal.

[0007] Optionally, in one embodiment of this application, the step of performing ensemble-averaged empirical mode decomposition on the time-frequency signal to be processed using CEEMDAN to obtain multiple initial intrinsic mode functions of the time-frequency signal to be processed includes: obtaining Gaussian white noise corresponding to the time-frequency signal to be processed; adding the Gaussian white noise to the time-frequency signal to be processed to obtain a Gaussian time-frequency signal to be processed after adding the Gaussian white noise; and performing ensemble-averaged empirical mode decomposition on the Gaussian time-frequency signal to be processed using CEEMDAN to obtain the multiple initial intrinsic mode functions.

[0008] Optionally, in one embodiment of this application, obtaining multiple final intrinsic mode functions (IMFs) that satisfy preset conditions from the multiple initial IMFs based on the signal analysis parameters and the multiple initial IMFs includes: calculating the spectral characteristics of each initial IMF through a target fast Fourier transform to obtain the spectral information of each initial IMF; determining the frequency components in the spectral information that satisfy preset amplitude conditions based on the signal analysis parameters and the spectral information; and obtaining the multiple final IMFs based on the frequency components.

[0009] Optionally, in one embodiment of this application, obtaining a plurality of final intrinsic mode functions (IMFs) satisfying preset conditions from the plurality of initial IMFs based on the signal analysis parameters and the plurality of initial IMFs includes: obtaining fitting parameters of the plurality of initial IMFs based on the plurality of initial IMFs; calculating fitting residuals of the plurality of initial IMFs based on the signal analysis parameters and the fitting parameters; and obtaining the plurality of final IMFs based on the fitting residuals.

[0010] Optionally, in one embodiment of this application, obtaining a plurality of final intrinsic mode functions (IMFs) satisfying preset conditions from the plurality of initial IMFs based on the signal analysis parameters and the plurality of initial IMFs includes: selecting target signal analysis parameters from the signal analysis parameters that satisfy preset parameter conditions; optimizing the target signal analysis parameters to obtain optimized target signal analysis parameters; and obtaining the plurality of final IMFs based on the optimized target signal analysis parameters and the plurality of initial IMFs.

[0011] Optionally, in one embodiment of this application, the step of fusing information on the plurality of final intrinsic mode functions to obtain fused intrinsic mode functions, and processing the time-frequency signal to be processed based on the fused intrinsic mode functions to obtain the processed time-frequency signal, includes: obtaining a stability evaluation index of the processed time-frequency signal; determining whether the processed time-frequency signal meets a preset stability evaluation condition based on the stability evaluation index; if the processed time-frequency signal does not meet the preset stability evaluation condition, then re-obtaining the plurality of final intrinsic mode functions until the processed time-frequency signal meets the preset stability condition.

[0012] A second aspect of this application provides a time-frequency signal processing apparatus based on CEEMDAN, comprising: a first generation module, configured to perform ensemble-averaged empirical mode decomposition on the time-frequency signal to be processed using CEEMDAN to obtain multiple initial intrinsic mode functions (IMFs) of the time-frequency signal to be processed; a second generation module, configured to perform time-frequency analysis on the multiple initial IMFs to generate signal analysis parameters of the time-frequency signal to be processed; an acquisition module, configured to acquire multiple final IMFs that satisfy preset conditions from the multiple initial IMFs based on the signal analysis parameters and the multiple initial IMFs; and a processing module, configured to perform information fusion on the multiple final IMFs to obtain fused IMFs, and process the time-frequency signal to be processed based on the fused IMFs to obtain a processed time-frequency signal.

[0013] Optionally, in one embodiment of this application, the first generation module includes: a first acquisition unit, configured to acquire Gaussian white noise corresponding to the time-frequency signal to be processed; a first generation unit, configured to add the Gaussian white noise to the time-frequency signal to be processed to obtain a Gaussian time-frequency signal to be processed after adding the Gaussian white noise; and a second generation unit, configured to perform ensemble-averaged empirical mode decomposition on the Gaussian time-frequency signal to be processed using CEEMDAN to obtain the plurality of initial intrinsic mode functions.

[0014] Optionally, in one embodiment of this application, the acquisition module includes: a third generation unit, configured to calculate the spectral characteristics of each initial intrinsic mode function through a target fast Fourier transform to obtain the spectral information of each initial intrinsic mode function; a determination unit, configured to determine the frequency components in the spectral information that satisfy a preset amplitude condition based on the signal analysis parameters and the spectral information; and a fourth generation unit, configured to obtain the plurality of final intrinsic mode functions based on the frequency components.

[0015] Optionally, in one embodiment of this application, the acquisition module includes: a fifth generation unit, configured to obtain fitting parameters of the plurality of initial intrinsic mode functions based on the plurality of initial intrinsic mode functions; a calculation unit, configured to calculate the fitting residuals of the plurality of initial intrinsic mode functions based on the signal analysis parameters and the fitting parameters; and a sixth generation unit, configured to obtain the plurality of final intrinsic mode functions based on the fitting residuals.

[0016] Optionally, in one embodiment of this application, the acquisition module includes: a selection unit, used to select target signal analysis parameters that meet preset parameter conditions from the signal analysis parameters; an optimization unit, used to optimize the target signal analysis parameters to obtain optimized target signal analysis parameters; and a seventh generation unit, used to obtain the plurality of final intrinsic mode functions based on the optimized target signal analysis parameters and the plurality of initial intrinsic mode functions.

[0017] Optionally, in one embodiment of this application, the processing module includes: a second acquisition unit, configured to acquire a stability evaluation index of the processed time-frequency signal; a judgment unit, configured to determine whether the processed time-frequency signal meets a preset stability evaluation condition based on the stability evaluation index; and a third acquisition unit, configured to reacquire the plurality of final intrinsic mode functions when the processed time-frequency signal does not meet the preset stability evaluation condition, until the processed time-frequency signal meets the preset stability condition.

[0018] A third aspect of this application provides an electronic device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the CEEMDAN-based time-frequency signal processing method as described in the above embodiments.

[0019] A fourth aspect of this application provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described CEEMDAN-based time-frequency signal processing method.

[0020] A fifth aspect of this application provides a computer program product, including a computer program that, when executed, implements the CEEMDAN-based time-frequency signal processing method described above.

[0021] This application embodiment utilizes CEEMDAN to perform ensemble-averaged empirical mode decomposition on the time-frequency signal to be processed, obtaining multiple initial intrinsic mode functions (IMFs). Time-frequency analysis is then performed on these initial IMFs to generate signal analysis parameters. Finally, multiple final IMFs satisfying certain conditions are obtained from the initial IMFs. These final IMFs are then fused to obtain a fused IMF, which is used to process the time-frequency signal to obtain a processed time-frequency signal. This provides more comprehensive and accurate data for further signal processing and analysis, and is more effective in processing nonlinear and non-stationary signals. It offers real-time performance and provides an efficient and flexible solution for the time-frequency characteristics of complex signals. It is applicable to the processing of large-scale datasets and provides advanced and practical technical means for signal analysis in multiple fields. Therefore, it solves the problems of related technologies, such as insufficient real-time and effectiveness in processing nonlinear and non-stationary signals, inapplicability to large-scale datasets, narrow application scope in practical processing, and inability to meet the actual needs of signal processing and analysis.

[0022] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

[0023] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein:

[0024] Figure 1 This is a flowchart illustrating a time-frequency signal processing method based on CEEMDAN according to an embodiment of this application;

[0025] Figure 2(a) is a partial flowchart of CEEMDAN signal decomposition according to an embodiment of this application;

[0026] Figure 2(b) is another part of the flowchart of CEEMDAN signal decomposition according to an embodiment of this application;

[0027] Figure 3 This is a block diagram of a CEEMDAN-based time-frequency signal processing device according to an embodiment of this application;

[0028] Figure 4 This is a schematic diagram of the structure of an electronic device provided according to an embodiment of this application. Detailed Implementation

[0029] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0030] The following description, with reference to the accompanying drawings, describes a time-frequency signal processing method and apparatus based on CEEMDAN according to embodiments of this application. To address the issues mentioned in the background art regarding the insufficient real-time and effectiveness of processing nonlinear and non-stationary signals, their inability to handle large-scale datasets, and their narrow application scope in practical processing, failing to meet the actual needs of signal processing and analysis, this application provides a time-frequency signal processing method based on CEEMDAN. In this method, CEEMDAN is used to perform ensemble-averaged empirical mode decomposition on the time-frequency signal to be processed, obtaining multiple initial intrinsic mode functions (EMFs). Time-frequency analysis is then performed on these initial EMFs to generate signal analysis parameters. Furthermore, multiple final EMFs satisfying certain conditions are obtained from the initial EMFs. These final EMFs are then fused to obtain a fused EMF, which is used to process the time-frequency signal to be processed, resulting in a processed time-frequency signal. This provides more comprehensive and accurate data for further signal processing and analysis, is more effective in processing nonlinear and non-stationary signals, and has real-time performance. It offers an efficient and flexible solution for the time-frequency characteristics of complex signals, is applicable to large-scale datasets, and provides advanced and practical technical means for signal analysis in multiple fields. This solves the problems in related technologies, such as insufficient real-time and effectiveness in processing nonlinear and non-stationary signals, inability to process large-scale datasets, narrow application scope in practical processing, and inability to meet the actual needs of signal processing and analysis.

[0031] Specifically, Figure 1 This is a flowchart of a time-frequency signal processing method based on CEEMDAN provided according to an embodiment of this application.

[0032] like Figure 1 As shown, the time-frequency signal processing method based on CEEMDAN includes the following steps:

[0033] In step S101, the empirical mode decomposition of the time-frequency signal to be processed is performed by ensemble averaging using CEEMDAN to obtain multiple initial intrinsic mode functions of the time-frequency signal to be processed.

[0034] It is understood that, in practical applications, time-frequency signal analysis is commonly used in fields such as audio processing, communication systems, radar systems, timekeeping, time synchronization, and satellite navigation. Considering that time-frequency signals not only contain the time or frequency information of the clock output, but also other signals formed due to environmental influences, signal propagation, clock aging, frequency drift, and other factors, signal processing methods are needed to decompose the time-frequency signal to be processed and remove interference signals such as periodic terms and quadratic terms to obtain a purer time-frequency signal.

[0035] Furthermore, in the embodiments of this application, the time and frequency signal to be processed can be a second pulse signal or a frequency signal (such as a 5MHz frequency signal, a 10MHz frequency signal, a 100MHz frequency signal, etc., which are not specifically limited in this application) output by an atomic clock (such as a rubidium clock, a cesium clock, a hydrogen clock, etc., which are not specifically limited in this application); it can also be time data or frequency data obtained by comparing two or more atomic clocks using a time interval comparator or a frequency comparator; it can also be a time series reflecting the operation of the atomic clock obtained by using GNSS (Global Navigation Satellite System) time transfer, satellite two-way time and frequency transfer, etc. The specific settings can be made by those skilled in the art according to the actual situation, and this application does not make specific limitations.

[0036] As one possible implementation, embodiments of this application can use CEEMDAN to perform ensemble-averaged empirical mode decomposition on the time-frequency signal to be processed, thereby obtaining multiple initial intrinsic mode functions.

[0037] Optionally, in one embodiment of this application, the empirical mode decomposition of the time-frequency signal to be processed is performed by CEEMDAN with ensemble averaging to obtain multiple initial intrinsic mode functions of the time-frequency signal to be processed. This includes: obtaining Gaussian white noise corresponding to the time-frequency signal to be processed; adding Gaussian white noise to the time-frequency signal to be processed to obtain a Gaussian time-frequency signal to be processed after adding Gaussian white noise; and performing empirical mode decomposition of the Gaussian time-frequency signal to be processed by CEEMDAN with ensemble averaging to obtain multiple initial intrinsic mode functions.

[0038] In some embodiments, Gaussian white noise can be added to the time-frequency signal to be processed to obtain a Gaussian time-frequency signal to be processed after adding Gaussian white noise. Empirical mode decomposition is performed on the Gaussian time-frequency signal to be processed, and geometric averaging is performed to obtain multiple initial intrinsic mode functions, so as to reduce the influence of noise and obtain the result of time-frequency analysis.

[0039] In step S102, time-frequency analysis is performed on multiple initial intrinsic mode functions to generate signal analysis parameters for the time-frequency signal to be processed.

[0040] As one possible implementation, embodiments of this application can perform time-frequency analysis on multiple initial intrinsic mode functions to obtain multiple signal analysis parameters such as period information, frequency information, and noise signal-to-noise ratio of the time-frequency signal to be processed. The signal analysis parameters can be set by those skilled in the art according to the actual situation, and this application does not impose specific limitations.

[0041] In step S103, based on signal analysis parameters and multiple initial intrinsic mode functions, multiple final intrinsic mode functions that satisfy preset conditions are obtained from the multiple initial intrinsic mode functions.

[0042] Those skilled in the art will understand that the embodiments of this application can analyze signal analysis parameters through an objective function, and then obtain multiple final intrinsic mode functions (IMFs) satisfying certain conditions from multiple initial IMFs. These certain conditions can be set by those skilled in the art according to actual circumstances, and this application does not impose specific limitations.

[0043] For example, in this application embodiment, the objective function can be used to determine whether the signal analysis parameters meet certain conditions. If the signal analysis parameters meet certain conditions, the corresponding initial intrinsic mode function is retained; otherwise, the corresponding initial intrinsic mode function is deleted. Thus, in this application embodiment, multiple final intrinsic mode functions that meet certain conditions can be obtained.

[0044] Optionally, in one embodiment of this application, based on signal analysis parameters and multiple initial intrinsic mode functions (IMFs), obtaining multiple final IMFs that satisfy preset conditions from the multiple initial IMFs includes: calculating the spectral characteristics of each initial IMF through a target fast Fourier transform to obtain the spectral information of each initial IMF; determining the frequency components in the spectral information that satisfy preset amplitude conditions based on the signal analysis parameters and the spectral information; and obtaining multiple final IMFs based on the frequency components.

[0045] In some embodiments, the present application can calculate the spectral characteristics of each initial intrinsic mode function, that is, perform a target fast Fourier transform on the initial intrinsic mode function to obtain the corresponding spectral information, and find the frequency components that satisfy a certain amplitude condition (such as maximum amplitude, etc., wherein the certain amplitude condition can be set by those skilled in the art according to the actual situation, and the present application does not impose specific limitations) in the spectral information, and then determine whether the amplitude satisfies a certain condition (such as less than or equal to a target significance threshold, wherein the target significance threshold can be set by those skilled in the art according to the actual situation, and the present application does not impose specific limitations).

[0046] In some embodiments of this application, if the amplitude meets certain conditions, namely, the amplitude is less than or equal to the target significance threshold, the initial intrinsic mode function is determined to have no significant periodicity, the corresponding initial intrinsic mode function is retained, and multiple final intrinsic mode functions are obtained.

[0047] In some embodiments of this application, if the amplitude does not meet certain conditions, i.e., the amplitude is greater than the target significance threshold, the initial intrinsic mode function is determined to have significant periodicity, the corresponding initial intrinsic mode function is deleted, and multiple final intrinsic mode functions are obtained.

[0048] Optionally, in one embodiment of this application, obtaining multiple final intrinsic mode functions (EMFs) that satisfy preset conditions from the multiple initial EMFs based on signal analysis parameters and multiple initial EMFs includes: obtaining fitting parameters of the multiple initial EMFs based on the multiple initial EMFs; calculating fitting residuals of the multiple initial EMFs based on the signal analysis parameters and the fitting parameters; and obtaining multiple final EMFs based on the fitting residuals.

[0049] In some embodiments, the present application can perform quadratic polynomial fitting on each initial intrinsic mode function and record the fitting parameters of multiple initial intrinsic mode functions, thereby calculating the fitting residual and determining whether the fitting residual meets certain conditions (such as being greater than or equal to a target threshold, wherein the target threshold can be set by those skilled in the art according to the actual situation, and the present application does not impose specific limitations).

[0050] In some embodiments of this application, if the fitting residuals meet certain conditions, namely, if the fitting residuals are greater than or equal to the target threshold, it is determined that the initial intrinsic mode function does not have obvious quadratic characteristics, and the corresponding initial intrinsic mode function is retained, thereby obtaining multiple final intrinsic mode functions.

[0051] In some embodiments of this application, if the fitting residual does not meet certain conditions, i.e. the fitting residual is less than the target threshold, it is determined that the initial intrinsic mode function has obvious quadratic characteristics, and the corresponding initial intrinsic mode function is deleted, thereby obtaining multiple final intrinsic mode functions.

[0052] Optionally, in one embodiment of this application, obtaining multiple final intrinsic mode functions (IMFs) that satisfy preset conditions from among the multiple initial IMFs based on signal analysis parameters and multiple initial IMFs includes: selecting target signal analysis parameters that satisfy preset parameter conditions from among the signal analysis parameters; optimizing the target signal analysis parameters to obtain optimized target signal analysis parameters; and obtaining multiple final IMFs based on the optimized target signal analysis parameters and multiple initial IMFs.

[0053] In some embodiments, the present application embodiments may add other filtering conditions or constraints according to actual application needs, such as selecting target signal analysis parameters that meet certain parameter conditions, such as specific signal characteristics, frequency range, noise level, etc. The present application does not impose specific restrictions. Furthermore, the present application embodiments optimize the selected target signal analysis parameters to obtain optimized target signal analysis parameters, thereby ensuring that the multiple final intrinsic mode functions obtained can effectively represent the actual physical mode of the signal.

[0054] In step S104, information fusion is performed on multiple final intrinsic mode functions to obtain fused intrinsic mode functions, and the time-frequency signal to be processed is processed based on the fused intrinsic mode functions to obtain the processed time-frequency signal.

[0055] As one possible implementation method, embodiments of this application perform information fusion on multiple final intrinsic mode functions to obtain fused intrinsic mode functions, and then process the time-frequency signal to be processed to obtain the processed time-frequency signal.

[0056] Optionally, in one embodiment of this application, information fusion is performed on multiple final intrinsic mode functions to obtain fused intrinsic mode functions, and the time-frequency signal to be processed is processed based on the fused intrinsic mode functions to obtain the processed time-frequency signal, including: obtaining a stability evaluation index of the processed time-frequency signal; determining whether the processed time-frequency signal meets a preset stability evaluation condition based on the stability evaluation index; if the processed time-frequency signal does not meet the preset stability evaluation condition, then multiple final intrinsic mode functions are re-obtained until the processed time-frequency signal meets the preset stability condition.

[0057] Furthermore, it should be noted that after obtaining the processed time-frequency signal, the embodiments of this application can also evaluate the stability of the processed time-frequency signal. The main content can be as follows: First, the embodiments of this application can obtain a stability evaluation index for the processed time-frequency signal, and then determine whether the processed time-frequency signal meets certain stability evaluation conditions. If the processed time-frequency signal does not meet certain stability evaluation conditions, multiple final intrinsic mode functions are re-obtained until the processed time-frequency signal meets the preset stability conditions. The certain stability evaluation conditions can be set by those skilled in the art according to actual conditions, and this application does not impose specific limitations.

[0058] Furthermore, in the embodiments of this application, stability evaluation metrics may include, but are not limited to, Allan variance, modified Allan variance, Hadamard variance, etc. This application does not impose specific limitations. These variance metrics can quantify the frequency variation of the oscillator at different time scales, thereby analyzing the stability of the oscillator. By analyzing the random fluctuations of the oscillator, they can distinguish different types of noise (e.g., white noise, random walk noise, etc., this application does not impose specific limitations) and reveal the stability performance of the oscillator under these noise conditions. Therefore, these three evaluation methods are widely used in fields such as atomic clocks and frequency synthesizers, providing a scientific basis for time-frequency signal processing.

[0059] Furthermore, in the embodiments of this application, Allan variance is a statistical method for evaluating the short-term stability of time-frequency signals. By analyzing the frequency changes within a time interval, it can effectively distinguish different types of random noise, and is particularly suitable for describing the stability of signals over a short period of time. Its calculation formula can be, but is not limited to, expressed as:

[0060]

[0061] Among them, y i It is the i-th relative frequency measurement value within the measurement (sampling) interval, where τ is the sampling interval and M is the number of consecutive measurements.

[0062] The modified Allan variance incorporates frequency information averaging, improving the ability to distinguish high-frequency noise and making it suitable for signal analysis with complex noise. Its calculation formula can be, but is not limited to, expressed as:

[0063]

[0064] Where M is the data length and m is the number of overlapping points or the size of the sub-interval. It is a parameter that controls the segmentation of time series processing. Specifically, it defines the number of samples used when calculating each sub-interval. It is mainly used to "segment" the time series so that the fluctuation of the signal at different time scales can be evaluated.

[0065] Hadamard variance focuses more on eliminating the effects of linear drift and is particularly effective for medium- to long-term stability assessment. Its calculation formula can be, but is not limited to, expressed as:

[0066]

[0067] The working principle of the time-frequency signal processing method based on CEEMDAN proposed in this application will be introduced below with reference to several specific embodiments.

[0068] Example 1:

[0069] Figure 2(a) is a partial flowchart of CEEMDAN signal decomposition according to an embodiment of this application.

[0070] Figure 2(b) is another part of the flowchart of CEEMDAN signal decomposition according to an embodiment of this application.

[0071] As shown in Figures 2(a) and 2(b), the main content of signal decomposition using CEEMDAN in this embodiment is as follows: First, a time-frequency signal to be processed, such as signal x, is selected, and different Gaussian white noises are added to x. Then, empirical mode decomposition is performed to obtain multiple initial intrinsic mode functions imf1(j), where i = 1, 2, ..., k, j = 1, 2, ..., n, n is the number of Gaussian white noises, and k is the number of redundant signals in the signal to be processed. These initial intrinsic mode functions imf1 are averaged to obtain a final intrinsic mode function IMF1, which is the final result output by CEEMDAN. Then, this final intrinsic mode function IMF1 is removed from signal x, and the above cycle is repeated until empirical mode decomposition can no longer decompose the residual signal, thus obtaining all final intrinsic mode functions.

[0072] Example 2: Time Signal Analysis

[0073] Experimental objective:

[0074] The experimental objective of this application embodiment is to verify the application effect of this application embodiment in time signal analysis, with a focus on the processing performance of nonlinear and non-stationary signals.

[0075] Experimental setup:

[0076] The experimental setup in this embodiment includes an atomic clock, a data acquisition device, CEEMDAN time and frequency data processing software, and a computer.

[0077] Experimental steps:

[0078] The experimental steps of this application embodiment are as follows: (1) Use an atomic clock to output a time signal to be processed containing nonlinear and non-stationary characteristics; (2) Input the output time signal to be processed into a data acquisition device to acquire signal data; (3) Use a time-frequency signal processing method based on CEEMDAN to process the acquired time signal to be processed, including steps such as ensemble average empirical mode decomposition, intrinsic mode function selection, and time-frequency analysis; (4) Observe the processed time-frequency data and analyze whether the instantaneous characteristics and spectral changes in the time signal to be processed are better captured; (5) By comparing with traditional methods (such as time domain analysis and frequency domain analysis), evaluate the superiority of this application embodiment in extracting the dynamic characteristics of the signal.

[0079] Experimental results:

[0080] The experimental results of this application's embodiments are as follows: In time signal analysis, this application's embodiments can better preserve the nonlinear and non-stationary properties of the signal, allowing for clearer observation of the signal's instantaneous changes and spectral characteristics in the time-frequency domain. Compared to traditional methods, this application's embodiments can more accurately reflect instantaneous events and frequency changes in the signal, confirming its advantages in time signal analysis.

[0081] Example 3: Frequency Signal Analysis

[0082] Experimental objective:

[0083] The experimental objective of this application embodiment is to verify the application effect of this application embodiment in frequency signal analysis, with particular attention to its processing performance for signals with rapidly changing and non-stationary frequencies.

[0084] Experimental setup:

[0085] The experimental setup in this application embodiment includes an atomic clock, a frequency comparator, CEEMDAN time-frequency data processing software, and a computer.

[0086] Experimental steps:

[0087] The experimental steps of this application embodiment are as follows: (1) using an atomic clock to output a frequency signal to be processed that has a fast frequency change and non-stationary characteristics; (2) using a frequency comparator to perform high-frequency sampling on the generated frequency signal to be processed to obtain high-frequency signal data; (3) using a time-frequency signal processing method based on CEEMDAN to process the collected time signal to be processed, including steps such as ensemble average empirical mode decomposition, intrinsic mode function selection, and time-frequency analysis; (4) observing the processed time-frequency data and analyzing whether it better captures the instantaneous frequency changes and spectral characteristics in the frequency signal to be processed; (5) by comparing with traditional methods (such as short-time Fourier transform), evaluating the superiority of this application embodiment in extracting the dynamic characteristics of high-frequency signals.

[0088] Experimental results:

[0089] The experimental results of the embodiments of this application show that: the embodiments of this application can better handle signals with rapid frequency changes and non-stationary frequencies in frequency signal analysis, making the instantaneous frequency changes and spectral characteristics of the signal more clearly observable in the time-frequency domain. Compared with traditional methods, the embodiments of this application can more accurately reflect the instantaneous frequency changes in the signal, confirming its advantages in frequency signal analysis.

[0090] Example 4: Processing data from a time-frequency comparison method for measuring gravitational potential

[0091] Experimental objective:

[0092] The experimental objective of this application embodiment is to verify whether this application embodiment can improve the accuracy of the gravity potential measurement data by time-frequency comparison.

[0093] Experimental setup:

[0094] The experimental setup in this embodiment includes: a time-frequency comparison measurement system, a high-precision atomic clock, a coaxial cable, a data acquisition device, CEEMDAN time-frequency data processing software, and a computer.

[0095] Experimental steps:

[0096] The experimental steps of this application embodiment are as follows: (1) Using a time-frequency comparison measurement system, time-frequency comparison is performed between two stations, and the gravity potential difference data, including the time-frequency comparison results, is calculated using relativistic methods; (2) The measurement system and data acquisition equipment are connected by a coaxial cable to collect time-frequency comparison data; (3) The time-frequency signal processing method based on CEEMDAN is used to process the collected time signal to be processed, including steps such as ensemble average empirical mode decomposition, intrinsic mode function selection, and time-frequency analysis; (4) The processed time-frequency data is observed to analyze whether the gravity potential change characteristics in the time-frequency comparison data are better captured; By comparing with traditional methods, the superiority of this application embodiment in extracting the dynamic characteristics of gravity potential change is evaluated.

[0097] Experimental results:

[0098] The experimental results of the embodiments of this application show that the embodiments of this application can better process gravity potential measurement data by time-frequency comparison, thereby improving the accuracy of gravity potential measurement. Compared with traditional methods, the embodiments of this application can more accurately reflect the various signal characteristics in the measurement, confirming its application advantages in processing gravity potential measurement data by time-frequency comparison.

[0099] The time-frequency signal processing method based on CEEMDAN proposed in this application can perform ensemble-averaged empirical mode decomposition on the time-frequency signal to be processed using CEEMDAN to obtain multiple initial intrinsic mode functions (IMFs). Time-frequency analysis is then performed on these initial IMFs to generate signal analysis parameters. Finally, multiple final IMFs satisfying certain conditions are obtained from the initial IMFs. These final IMFs are then fused to obtain a fused IMF, which is used to process the time-frequency signal to obtain the processed time-frequency signal. This provides more comprehensive and accurate data for further signal processing and analysis, is more effective in processing nonlinear and non-stationary signals, and has real-time performance. It provides an efficient and flexible solution for the time-frequency characteristics of complex signals and is applicable to the processing of large-scale datasets. It provides advanced and practical technical means for signal analysis in multiple fields. Therefore, it solves the problems of related technologies, such as insufficient real-time and effectiveness in processing nonlinear and non-stationary signals, inability to process large-scale datasets, narrow application scope in practical processing, and inability to meet the actual needs of signal processing and analysis.

[0100] Next, referring to the accompanying drawings, a time-frequency signal processing apparatus based on CEEMDAN according to an embodiment of this application is described.

[0101] Figure 3 This is a block diagram of a CEEMDAN-based time-frequency signal processing apparatus according to an embodiment of this application.

[0102] like Figure 3 As shown, the CEEMDAN-based time-frequency signal processing device 30 includes: a first generation module 100, a second generation module 200, an acquisition module 300, and a processing module 400.

[0103] The first generation module 100 is used to perform ensemble-averaged empirical mode decomposition on the time-frequency signal to be processed using CEEMDAN to obtain multiple initial intrinsic mode functions of the time-frequency signal to be processed.

[0104] The second generation module 200 is used to perform time-frequency analysis on multiple initial intrinsic mode functions to generate signal analysis parameters for the time-frequency signal to be processed.

[0105] The acquisition module 300 is used to acquire multiple final intrinsic mode functions that satisfy preset conditions from multiple initial intrinsic mode functions based on signal analysis parameters and multiple initial intrinsic mode functions.

[0106] The processing module 400 is used to fuse multiple final intrinsic mode functions to obtain fused intrinsic mode functions, and to process the time-frequency signal to be processed based on the fused intrinsic mode functions to obtain the processed time-frequency signal.

[0107] Optionally, in one embodiment of this application, the first generation module 100 includes: a first acquisition unit, a first generation unit, and a second generation unit.

[0108] The first acquisition unit is used to acquire the Gaussian white noise corresponding to the time-frequency signal to be processed.

[0109] The first generation unit is used to add Gaussian white noise to the time-frequency signal to be processed, so as to obtain the Gaussian time-frequency signal to be processed after adding Gaussian white noise to the time-frequency signal to be processed.

[0110] The second generation unit is used to perform ensemble-averaged empirical mode decomposition on the Gaussian time-frequency signal to be processed using CEEMDAN to obtain multiple initial intrinsic mode functions.

[0111] Optionally, in one embodiment of this application, the acquisition module 300 includes: a third generation unit, a determination unit, and a fourth generation unit.

[0112] The third generation unit is used to calculate the spectral characteristics of each initial intrinsic mode function through the target fast Fourier transform, so as to obtain the spectral information of each initial intrinsic mode function.

[0113] The determination unit is used to determine the frequency components in the spectrum information that meet the preset amplitude conditions based on signal analysis parameters and spectrum information.

[0114] The fourth generation unit is used to obtain multiple final intrinsic mode functions based on frequency components.

[0115] Optionally, in one embodiment of this application, the acquisition module 300 includes: a fifth generation unit, a calculation unit, and a sixth generation unit.

[0116] The fifth generation unit is used to obtain fitting parameters for multiple initial intrinsic mode functions based on multiple initial intrinsic mode functions.

[0117] The computational unit is used to calculate the fitting residuals of multiple initial intrinsic mode functions based on signal analysis parameters and fitting parameters.

[0118] The sixth generation unit is used to obtain multiple final intrinsic mode functions based on the fitting residuals.

[0119] Optionally, in one embodiment of this application, the acquisition module 300 includes: a selection unit, an optimization unit, and a seventh generation unit.

[0120] The selection unit is used to select target signal analysis parameters that meet the preset parameter conditions from the signal analysis parameters.

[0121] The optimization unit is used to optimize the target signal analysis parameters to obtain the optimized target signal analysis parameters.

[0122] The seventh generation unit is used to obtain multiple final intrinsic mode functions based on the optimized target signal analysis parameters and multiple initial intrinsic mode functions.

[0123] Optionally, in one embodiment of this application, the processing module 400 includes: a second acquisition unit, a judgment unit, and a third acquisition unit.

[0124] The second acquisition unit is used to acquire stability evaluation indicators for the processed time-frequency signals.

[0125] The judgment unit is used to determine whether the processed time-frequency signal meets the preset stability evaluation conditions based on the stability evaluation index.

[0126] The third acquisition unit is used to reacquire multiple final intrinsic mode functions when the processed time-frequency signal does not meet the preset stability evaluation conditions, until the processed time-frequency signal meets the preset stability conditions.

[0127] It should be noted that the foregoing explanation of the CEEMDAN-based time-frequency signal processing method embodiment also applies to the CEEMDAN-based time-frequency signal processing device of this embodiment, and will not be repeated here.

[0128] The CEEMDAN-based time-frequency signal processing device proposed in this application can perform ensemble-averaged empirical mode decomposition on the time-frequency signal to be processed using CEEMDAN to obtain multiple initial intrinsic mode functions (IMFs). Time-frequency analysis is then performed on these initial IMFs to generate signal analysis parameters. Finally, multiple final IMFs satisfying certain conditions are obtained from the initial IMFs. These final IMFs are then fused to obtain fused IMFs, which are used to process the time-frequency signal to obtain the processed time-frequency signal. This provides more comprehensive and accurate data for further signal processing and analysis, and is more effective in processing nonlinear and non-stationary signals. It is real-time and provides an efficient and flexible solution for the time-frequency characteristics of complex signals. It is applicable to the processing of large-scale datasets and provides advanced and practical technical means for signal analysis in multiple fields. Therefore, it solves the problems of related technologies, such as insufficient real-time and effectiveness in processing nonlinear and non-stationary signals, inability to process large-scale datasets, narrow application scope in practical processing, and inability to meet the actual needs of signal processing and analysis.

[0129] Figure 4 This is a schematic diagram of the structure of an electronic device provided according to an embodiment of this application. The electronic device may include:

[0130] The memory 401, the processor 402, and the computer program stored on the memory 401 and capable of running on the processor 402.

[0131] When the processor 402 executes the program, it implements the time-frequency signal processing method based on CEEMDAN provided in the above embodiments.

[0132] Furthermore, electronic devices also include:

[0133] Communication interface 403 is used for communication between memory 401 and processor 402.

[0134] The memory 401 is used to store computer programs that can run on the processor 402.

[0135] The memory 401 may include high-speed RAM memory, and may also include non-volatile memory, such as at least one disk storage device.

[0136] If the memory 401, processor 402, and communication interface 403 are implemented independently, then the communication interface 403, memory 401, and processor 402 can be interconnected via a bus to complete communication between them. The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized into address buses, data buses, control buses, etc. For ease of representation, Figure 4 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0137] Optionally, in a specific implementation, if the memory 401, processor 402, and communication interface 403 are integrated on a single chip, then the memory 401, processor 402, and communication interface 403 can communicate with each other through an internal interface.

[0138] Processor 402 may be a central processing unit (CPU), an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of this application.

[0139] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described CEEMDAN-based time-frequency signal processing method.

[0140] This application also provides a computer program product, including a computer program that, when executed, implements the above-described CEEMDAN-based time-frequency signal processing method.

[0141] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0142] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "N" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0143] Any process or method described in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or N executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.

[0144] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0145] It should be understood that the various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, the N steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. If implemented in hardware, as in another embodiment, it can be implemented using any one or more of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0146] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

[0147] Furthermore, the functional units in the various embodiments of this application can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0148] The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of this application.

Claims

1. A time-frequency signal processing method based on CEEMDAN, characterized in that, Includes the following steps: The time-frequency signal to be processed is subjected to ensemble-averaged empirical mode decomposition (CEEMDAN) using adaptive noise-complete ensemble empirical mode decomposition (CEMDAN) to obtain multiple initial intrinsic mode functions (EMFs) of the signal. The time and frequency signals to be processed include second pulse signals or frequency signals output by atomic clocks, time data or frequency data obtained by comparing two or more atomic clocks using time interval comparators and frequency comparators, and time series reflecting the operation of atomic clocks obtained by using global navigation satellite system time transfer and satellite two-way time and frequency transfer. Time-frequency analysis is performed on the plurality of initial intrinsic mode functions to generate signal analysis parameters for the time-frequency signal to be processed; Based on the signal analysis parameters and the plurality of initial intrinsic mode functions, a plurality of final intrinsic mode functions that satisfy preset conditions are obtained from the plurality of initial intrinsic mode functions, wherein fitting parameters of the plurality of initial intrinsic mode functions are obtained based on the plurality of initial intrinsic mode functions; The fitting residuals of the plurality of initial intrinsic mode functions are calculated based on the signal analysis parameters and the fitting parameters; The plurality of final intrinsic mode functions are obtained based on the fitting residuals; Information fusion is performed on the multiple final intrinsic mode functions to obtain fused intrinsic mode functions, and the time-frequency signal to be processed is processed based on the fused intrinsic mode functions to obtain the processed time-frequency signal. Obtain the stability evaluation index of the processed time-frequency signal; Based on the stability evaluation index, determine whether the processed time-frequency signal meets the preset stability evaluation conditions; If the processed time-frequency signal does not meet the preset stability evaluation conditions, the plurality of final intrinsic mode functions are reacquired until the processed time-frequency signal meets the preset stability evaluation conditions.

2. The method according to claim 1, characterized in that, The step of performing ensemble-averaged empirical mode decomposition on the time-frequency signal to be processed using the adaptive noise-complete ensemble empirical mode decomposition (CEEMDAN) to obtain multiple initial intrinsic mode functions (EMFs) of the time-frequency signal to be processed includes: Obtain the Gaussian white noise corresponding to the time-frequency signal to be processed; The Gaussian white noise is added to the time-frequency signal to be processed to obtain the Gaussian time-frequency signal to be processed after adding the Gaussian white noise to the time-frequency signal to be processed. The Gaussian time-frequency signal to be processed is subjected to ensemble-averaged empirical mode decomposition using CEEMDAN to obtain the multiple initial intrinsic mode functions.

3. The method according to claim 1, characterized in that, The step of obtaining multiple final intrinsic mode functions (IMFs) that satisfy preset conditions from the multiple initial IMFs based on the signal analysis parameters and the multiple initial IMFs includes: The spectral characteristics of each initial intrinsic mode function are calculated by the target fast Fourier transform to obtain the spectral information of each initial intrinsic mode function; Based on the signal analysis parameters and the spectrum information, determine the frequency components in the spectrum information that satisfy the preset amplitude condition; The plurality of final intrinsic mode functions are obtained based on the frequency components.

4. The method according to claim 1, characterized in that, The step of obtaining multiple final intrinsic mode functions (IMFs) that satisfy preset conditions from the multiple initial IMFs based on the signal analysis parameters and the multiple initial IMFs includes: Select the target signal analysis parameters from the signal analysis parameters that meet the preset parameter conditions; The target signal analysis parameters are optimized to obtain the optimized target signal analysis parameters. Based on the optimized target signal analysis parameters and the plurality of initial intrinsic mode functions, the plurality of final intrinsic mode functions are obtained.

5. A time-frequency signal processing device based on CEEMDAN, characterized in that, include: The first generation module is used to perform ensemble-averaged empirical mode decomposition on the time-frequency signal to be processed using CEEMDAN to obtain multiple initial intrinsic mode functions of the time-frequency signal to be processed, wherein... The time and frequency signals to be processed include second pulse signals or frequency signals output by atomic clocks, time data or frequency data obtained by comparing two or more atomic clocks using time interval comparators and frequency comparators, and time series reflecting the operation of atomic clocks obtained by using global navigation satellite system time transfer and satellite two-way time and frequency transfer. The second generation module is used to perform time-frequency analysis on the plurality of initial intrinsic mode functions to generate signal analysis parameters for the time-frequency signal to be processed. The acquisition module is used to acquire, based on the signal analysis parameters and the plurality of initial intrinsic mode functions, a plurality of final intrinsic mode functions that satisfy preset conditions from the plurality of initial intrinsic mode functions, wherein, The fitting parameters of the multiple initial intrinsic mode functions are obtained based on the multiple initial intrinsic mode functions; The fitting residuals of the plurality of initial intrinsic mode functions are calculated based on the signal analysis parameters and the fitting parameters; The plurality of final intrinsic mode functions are obtained based on the fitting residuals; The processing module is used to fuse the multiple final intrinsic mode functions to obtain the fused intrinsic mode functions, and to process the time-frequency signal to be processed based on the fused intrinsic mode functions to obtain the processed time-frequency signal. It is also used to: obtain the stability evaluation index of the processed time-frequency signal. Based on the stability evaluation index, it is determined whether the processed time-frequency signal meets the preset stability evaluation conditions. If the processed time-frequency signal does not meet the preset stability evaluation conditions, the plurality of final intrinsic mode functions are reacquired until the processed time-frequency signal meets the preset stability evaluation conditions.

6. An electronic device, characterized in that, include: The memory, the processor, and the computer program stored in the memory and executable on the processor, the processor executing the program to implement the CEEMDAN-based time-frequency signal processing method as described in any one of claims 1-4.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, The program is executed by the processor to implement the CEEMDAN-based time-frequency signal processing method as described in any one of claims 1-4.

8. A computer program product, characterized in that, Includes a computer program, which, when executed, is used to implement the CEEMDAN-based time-frequency signal processing method as described in any one of claims 1-4.

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