Noise reduction processing method for dynamically changing signals
By constructing a multidimensional feature space and a high-order differential equation model, the problem of poor noise reduction effect for non-stationary, high-noise signals in existing technologies is solved, achieving effective noise reduction and feature preservation of signals, and improving signal-to-noise ratio and adaptability.
Patent Information
- Application Number
- CN202511425286.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-09-30
- Publication Date
- 2026-02-17
AI Technical Summary
Existing signal denoising methods are ineffective when dealing with non-stationary, high-noise dynamic signals, and are highly dependent on the statistical characteristics of the signal, making it difficult to effectively remove noise interference.
A multidimensional feature space is constructed, a high-order differential equation model for noise suppression is established, and the model is solved by combining stochastic process theory. The model is then transformed back to the original signal space through inverse mapping. The time-frequency features of the signal are extracted by using a sliding window, weighted summation, and complex exponential function, thereby reducing the dependence on the statistical properties of the signal.
It improves the noise reduction effect on non-stationary, high-noise dynamic signals, increases the signal-to-noise ratio by 15dB, retains important signal characteristics, and enhances adaptability and robustness.
Smart Images
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Abstract
Description
Technical Field
[0001] This invention relates to the field of signal processing technology, and more specifically to a noise reduction method for dynamically changing signals. Background Technology
[0002] In modern signal processing, dynamic signals are often affected by various types of noise, which may originate from the environment, the equipment itself, and the transmission process. The presence of noise can severely impact the accuracy of signal analysis and the effectiveness of subsequent processing.
[0003] Existing signal denoising methods mainly include filtering, wavelet transform, and Kalman filtering. While filtering is simple to implement, it is less effective at denoising non-stationary signals. Wavelet transform is prone to pseudo-Gibbs phenomenon when dealing with abrupt signals. Kalman filtering requires knowledge of the statistical characteristics of the signal and noise, which limits its applicability in practical applications. Summary of the Invention
[0004] In view of the shortcomings of the existing technology, the purpose of this invention is to provide a dynamic signal denoising processing method based on a complex mathematical model, so as to improve the denoising effect on non-stationary, high-noise dynamic signals, while reducing the dependence on signal statistical characteristics.
[0005] To achieve the above objectives, the present invention provides the following technical solution: a noise reduction method for dynamically changing signals, comprising the following steps: Step 1: Preprocess the acquired dynamic signals and convert them into discrete time series; Step 2: Construct a multidimensional feature space and map the discrete time series to this feature space; Step 3: Establish a high-order differential equation model for noise suppression in the multidimensional feature space; Step four: Solve the higher-order differential equation model using stochastic process theory; Step 5: The solution is converted back to the original signal space through inverse mapping to obtain the denoised dynamic signal.
[0006] As a further improvement of the present invention, the specific method for preprocessing the acquired dynamic signal in step one is as follows: A segment of radar dynamic echo signal was acquired, which was subject to strong Gaussian white noise interference, with a signal-to-noise ratio of 5dB. The acquired continuous signal was discretized, and the sampling frequency was 1000Hz to obtain the length... Discrete time series .
[0007] As a further improvement of the present invention, the specific method of multi-dimensional feature space mapping in step two is as follows: setting the feature space dimension Window length The mapping coefficients were determined through experiments. angular frequency The value of , where exist Randomly generated within the range, exist Values can be taken within a range; based on the mapping function. Discrete time series Mapping to a 5-dimensional feature space, we get ; in, Indicates the window Summation operation is performed on each signal value; These are weighting coefficients, used to adjust the contribution of signal values at different times to the feature components; For the first in the window The signal value at each moment; It is a complex exponential function, which introduces frequency characteristics, allowing the characteristic components to reflect the signal's features at different frequencies. This determines the frequency of the complex exponential function.
[0008] As a further improvement to the present invention, the specific method for establishing the higher-order differential equation model in step three is as follows: setting the order of the higher-order differential equation. The coefficients of the differential equation are set by empirical values. ,in , , , Regularization parameters attenuation coefficient Establish such as The higher-order differential equation model shown; Among them, the first item on the left For higher-order derivative terms, Represents the eigenvector components after noise reduction Regarding time First derivative, This term is used to capture the corresponding coefficients. Dynamic change characteristics; second item It is an integral term. This is a regularization parameter used to control the strength of the integral term. Indicates to The weighted integral is performed, with the weights decaying exponentially over time, and the decay coefficient is... ; the right side of the equation These are the eigenvector components after mapping.
[0009] As a further improvement to the present invention, the specific method for solving the high-order differential equation model in step four is as follows: assuming the noise follows a mean of 0 and a variance of... The Gaussian distribution was used, and the maximum likelihood estimation method was employed to estimate the unknown parameters in the model. Then, the Runge-Kutta method was used to numerically solve the higher-order differential equations, yielding the results. .
[0010] As a further improvement to the present invention, the specific method for obtaining the denoised dynamic signal by inverse mapping back to the original signal space in step five is as follows: Set the inverse mapping coefficient To satisfy The Gaussian function is chosen as the basis function. According to the inverse mapping function ,Will Converting back to the original signal space yields the denoised radar dynamic echo signal. ; in, Indicates to Summing the characteristic components; These are the weighting coefficients of the inverse mapping, used to adjust the contribution of different feature components in reconstructing the original signal; These are basis functions, the selection of which is related to the characteristics of the signal and is used to better match the features of the original signal; These are the feature vector components after noise reduction processing.
[0011] The beneficial effects of this invention include the construction of a unique multidimensional feature space mapping function. This function combines sliding window, weighted summation, and complex exponential function, which can fully extract the time-frequency features of dynamic signals, laying a solid foundation for subsequent noise reduction processing. Compared with traditional feature mapping methods, it can better adapt to the dynamic changes of signals. A noise suppression model integrating higher-order differential equations and integral terms is established. Higher-order differential equations can capture the higher-order variation characteristics of signals, while integral terms introduce smoothing constraints in the time dimension, effectively balancing the contradiction between signal noise reduction and detail preservation, and improving the ability to suppress complex noise. By combining stochastic process theory with the solution of higher-order differential equations, and determining model parameters through the maximum likelihood estimation method, the reliance on prior knowledge of signal and noise statistical properties is reduced, enhancing the adaptability and robustness of the method. Detailed Implementation
[0012] The present invention will be further described in detail below with reference to the given embodiments.
[0013] This embodiment of a noise reduction method for dynamically changing signals includes the following steps: Step 1: Preprocess the acquired dynamic signals and convert them into discrete time series; Step 2: Construct a multidimensional feature space and map the discrete time series to this feature space; Step 3: Establish a high-order differential equation model for noise suppression in the multidimensional feature space; Step four: Solve the higher-order differential equation model using stochastic process theory; Step 5: The solution is converted back to the original signal space through inverse mapping to obtain the denoised dynamic signal.
[0014] Furthermore, the above five steps are described in detail as follows: In step one, the acquired dynamic signal is preprocessed and converted into a discrete time series. ,in , The length of the signal is determined by acquiring a segment of radar dynamic echo signal, which is subject to strong Gaussian white noise interference with a signal-to-noise ratio of 5dB. The acquired continuous signal is discretized at a sampling frequency of 1000Hz to obtain the length. Discrete time series .
[0015] In step two, a multidimensional feature space is constructed, which integrates the discrete time series. This is mapped onto the feature space. Let the dimension of the feature space be . The mapping function is ,in , These are the components of the mapped feature vector. The mapping function satisfies the following relationship: ; in, For window length, For mapping coefficients, Angular frequency, The imaginary unit, specifically: setting the dimension of the feature space. Window length The mapping coefficients were determined experimentally. angular frequency The value of , where exist Randomly generated within the range, exist Values are taken within a range. Based on the mapping function. Discrete time series Mapping to a 5-dimensional feature space yields... The mapping function used above is used to map the original discrete-time series. The first one mapped to the multidimensional feature space Each component .in, Indicates the window Summation operation is performed on each signal value; These are weighting coefficients, used to adjust the contribution of signal values at different times to the feature components; For the first in the window The signal value at each moment; It is a complex exponential function, which introduces frequency characteristics, allowing the characteristic components to reflect the signal's features at different frequencies. This determines the frequency of the complex exponential function. Through such a mapping, a one-dimensional time series signal can be converted into a vector with multi-dimensional time-frequency characteristics, which facilitates subsequent noise processing.
[0016] In step three, a high-order differential equation model for noise suppression is established in the multidimensional feature space. Let the denoised feature vector components be... Then the following condition is met: ; in, Let be the order of the differential equation. The coefficients of the differential equation, For regularization parameters, The attenuation coefficient is... For time variables, specifically, setting the order of the higher-order differential equation. The coefficients of the differential equation are set by empirical values. ,in , , , Regularization parameters attenuation coefficient Establish such as The high-order differential equation model shown is the core model for noise suppression in a multidimensional feature space. The first term on the left... For higher-order derivative terms, where Represents the eigenvector components after noise reduction Regarding time First derivative, This term is used to capture the corresponding coefficients. Dynamic change characteristics; second item It is an integral term. This is a regularization parameter used to control the strength of the integral term. Indicates to The weighted integral is performed, and the weights decay exponentially over time (the decay coefficient is...). The integral term serves to smooth the signal and suppress noise; the right side of the equation... These are the mapped eigenvector components. This equation allows for the effective removal of noise while preserving the important features of the signal.
[0017] In step four, the higher-order differential equation model is solved using stochastic process theory. It is assumed that the noise follows a pattern with a mean of 0 and a variance of... The Gaussian distribution is used to determine the unknown parameters in the equation through the maximum likelihood estimation method, and then the numerical solution method is employed to obtain the solution. Specifically, we assume that the noise follows a mean of 0 and a variance of 0. The Gaussian distribution was used, and the maximum likelihood estimation method was employed to estimate the unknown parameters in the model. Then, the Runge-Kutta method was used to numerically solve the higher-order differential equations, yielding the results. .
[0018] In step five, the solution obtained... By inverse mapping and transformation back to the original signal space, the denoised dynamic signal is obtained. The inverse mapping function is ,satisfy: in, For inverse mapping coefficients, For basis functions, specifically, setting the inverse mapping coefficients. To satisfy The Gaussian function is chosen as the basis function. According to the inverse mapping function ,Will Converting back to the original signal space yields the denoised radar dynamic echo signal. The inverse mapping function formula mentioned above is used to convert the denoised feature vector components... Converting back to the original signal space yields the denoised dynamic signal. .in, Indicates to Summing the characteristic components; These are the weighting coefficients of the inverse mapping, used to adjust the contribution of different feature components in reconstructing the original signal; These are basis functions, the selection of which is related to the characteristics of the signal and is used to better match the features of the original signal; These are the feature vector components after noise reduction. Through this inverse mapping, the result processed in the multidimensional feature space can be restored to a one-dimensional time series signal, yielding the final noise-reduced signal.
[0019] In summary, the noise reduction method for dynamically changing signals in this embodiment improves the signal-to-noise ratio of the processed signal by 15dB and better preserves the target feature information in the radar echo signal.
[0020] In practical applications, the above noise reduction methods can be applied to multiple fields: In wireless communication, signals are affected by factors such as multipath fading and the Doppler effect during transmission, leading to severe distortion and noise interference in the received signal, especially in high-speed moving scenarios where signal non-stationarity is more pronounced. The dynamic signal denoising method of this invention can effectively reduce noise in received communication signals. By constructing a multi-dimensional feature space, fully extracting the signal features at different frequencies and times, and then using a high-order differential equation model to suppress noise, the bit error rate of the communication signal can be reduced, improving communication quality and reliability, and ensuring the accuracy of information transmission.
[0021] In medical signal detection such as electrocardiograms (ECG) and electroencephalograms (EEG), physiological activities and the detection equipment itself introduce a significant amount of noise. This noise can mask important physiological signal characteristics, affecting the accuracy of disease diagnosis. The method of this invention can be applied to noise reduction processing of medical signals. Because it can better preserve the detailed features of the signal, in ECG signal processing, it can clearly display key waveforms such as the P wave, QRS complex, and T wave, helping doctors to more accurately determine whether cardiac function is normal. For EEG signals, it can effectively remove noise interference from electromyography (EMG) and electrooculography (EOG), making the rhythm and waveform characteristics of brain waves more obvious, providing a more reliable basis for the diagnosis of neurological diseases. Medical signals processed using this method can improve the diagnostic accuracy of doctors.
[0022] In the field of sonar, sonar systems are affected by various noises during underwater detection, such as marine environmental noise and ship noise, which can submerge the target echo signal and affect the detection and identification of underwater targets. The noise reduction method of this invention is applicable to sonar signal processing. It can handle non-stationary sonar signals in high-noise environments. By performing multi-dimensional feature mapping and high-order differential equation noise reduction on the sonar echo signal, it can enhance the strength of the target signal, reduce noise interference, increase the detection range of the sonar system for underwater targets, improve the accuracy of target identification, and reduce false positives and false negatives.
[0023] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.
Claims
1. A method for noise reduction processing of a dynamic signal, the method comprising: The method comprises the following steps: Step one, pre-processing the collected dynamic signal and converting it into a discrete time series; Step two, constructing a multi-dimensional feature space and mapping the discrete time series into the feature space; Step three, establishing a high-order differential equation model for noise suppression in the multi-dimensional feature space; Step four, solving the high-order differential equation model in combination with the random process theory; Step five, converting the solved result back to the original signal space through inverse mapping to obtain the dynamic signal after noise reduction.
2. The noise reduction processing method for a dynamically changing signal according to claim 1, characterized by: The specific manner of pre-processing the collected dynamic signal in the step one is as follows: A radar dynamic echo signal is collected, which is interfered by strong Gaussian white noise and has a signal-to-noise ratio of 5dB. The collected continuous signal is discretized to obtain a discrete time sequence with a length of 1000Hz and a sampling frequency of 1000Hz. . 3. The noise reduction processing method for a dynamically changing signal according to claim 1 or 2, characterized by: The specific way of the multi-dimensional feature space mapping in the second step is as follows: setting the feature space dimension , the window length , determining the mapping coefficient through experiment , the angular frequency , wherein is randomly generated in the range of , and takes the value in the range of ; according to the mapping function , the discrete time sequence is mapped to the 5-dimensional feature space, and is obtained; wherein, represents a summation operation on the signal values within the window; is a weight coefficient, used to adjust the contribution of the signal values at different time instants in the feature component; is the signal value at the th time instant within the window; is a complex exponential function, which introduces frequency characteristics, so that the feature component can reflect the characteristics of the signal at different frequencies, determines the frequency of the complex exponential function. 4. The noise reduction processing method for a dynamically changing signal according to claim 1 or 2, characterized by: The specific way of establishing the high-order differential equation model in the third step is as follows: setting the order of the high-order differential equation , setting the differential equation coefficients by empirical values , wherein , , , ; the regularization parameter , the attenuation coefficient ; establishing the high-order differential equation model as shown in . where the first term on the left is a high-order derivative term, represents the feature vector component after noise reduction with respect to time of order , is the corresponding coefficient, which is used to capture the dynamic variation characteristics; the second term is an integral term, is a regularization parameter, which is used to control the strength of the integral term, represents the weighted integral of , and the weight decays exponentially with time, with the decay coefficient ; the right side of the equation is the mapped feature vector component.
5. The noise reduction processing method for a dynamically changing signal according to claim 1 or 2, characterized by: The specific way of solving the high-order differential equation model in step four is as follows: assuming that the noise obeys a Gaussian distribution with a mean of 0 and a variance , unknown parameters in the model are estimated by using a maximum likelihood estimation method, and then the high-order differential equation is numerically solved by using a Runge-Kutta method to obtain .
6. The noise reduction processing method for a dynamically changing signal according to claim 1 or 2, characterized by: The specific manner of converting back to the original signal space through inverse mapping to obtain the dynamic signal after noise reduction in the step five is as follows: Setting inverse mapping coefficients , so that it satisfies , select the Gaussian function as the basis function . According to the inverse mapping function , convert back to the original signal space to obtain the radar dynamic echo signal after noise reduction ; wherein, represents the sum over characteristic components; is a weight coefficient of the inverse mapping, which is used to adjust the contribution of different characteristic components in reconstructing the original signal; is a basis function, which is selected in relation to the characteristics of the signal, for better matching the characteristics of the original signal; is the characteristic vector component after denoising.