Signal reconstruction method based on time-varying filter
Through the signal reconstruction method based on time-varying filters, using time-frequency analysis and Bayesian law to process non-stable signals, the problem of poor non-stable signal reconstruction in the prior art is solved, and more accurate signal reconstruction and interference suppression is achieved.
Patent Information
- Application Number
- CN202411620486.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-14
- Publication Date
- 2025-02-25
AI Technical Summary
The prior art is difficult to effectively reconstruct non-stable signals of changing frequency, resulting in poor estimation effects.
A signal reconstruction method based on time-varying filter is adopted, a random model is established through time-frequency analysis, model parameters are estimated, and a time-varying Wiener filter is constructed based on Bayesian law, and the reconstructed non-stable signal is obtained through anti-time-varying transformation.
This method can reconstruct non-steady state signals more accurately, overcome the limitations of Wiener filtering when processing non-steady state signals, and significantly improve the quality and accuracy of signal reconstruction.
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Figure CN119513584A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of signal processing, and in particular to a signal reconstruction method based on a time-varying filter. Background Art
[0002] In the field of modern signal processing, the reconstruction of non-stationary periodic signals is an important task, especially in complex environments subject to interference. Non-stationary signals are widely present in vibration signals, radar communications, and biological signal processing. However, in practical applications, signals are often subject to various types of interference, such as random noise, harmonic distortion, and sudden interference, which makes accurate reconstruction of signals extremely challenging. To solve this problem, time-varying filters, as a tool for dynamically adjusting filtering characteristics, have shown unique advantages.
[0003] The classic Wiener filter technology performs well in processing the estimation of signals with fixed periodic frequencies. Its excellent noise suppression and signal reconstruction capabilities have been widely used and recognized in both the time domain and the frequency domain. In the time domain, the Wiener filter operation can be expressed as a convolution, which is very effective for the estimation of periodic and stable signals. In the frequency domain, it can be expressed as a product with the complex filter gain function, thereby improving the clarity and accuracy of the signal. However, these methods all assume that the frequency of the signal is fixed and periodic, which may lead to poor estimation results when facing non-stationary signals with varying frequencies in reality. In order to overcome the shortcomings of existing non-stationary signal reconstruction techniques, a signal reconstruction method based on time-varying filters is proposed. Summary of the invention
[0004] The present invention provides a signal reconstruction method based on a time-varying filter, which solves the technical problem that a poor estimation effect may be caused when a non-steady-state signal with a changing frequency is present in reality.
[0005] According to one aspect of the present disclosure, a signal reconstruction method based on a time-varying filter is provided, the method comprising: Step 1: Perform time-frequency analysis on the disturbed non-stationary signal to obtain the time-frequency spectrum; Step 2: Establish a random model based on the time-frequency spectrum of the signal and estimate the model parameters of the random model; Step 3: Construct a time-varying Wiener filter based on Bayes' theorem; Step 4: Obtain the reconstructed non-stationary signal through inverse time-frequency transform.
[0006] In a possible implementation, the step 1 of performing time-frequency analysis on the disturbed non-steady-state signal to obtain a time-frequency spectrum includes: 1-1: Collecting non-steady-state signals of the target object , where T is the number of time points of a single signal sample; 1-2: Select a window function ω(t) to collect the non-steady-state signal The result of the short-time Fourier transform (STFT) is a time-frequency matrix, in which each column represents the spectrum within a window, and each column represents how a frequency changes over time. The short-time Fourier transform conversion formula is: (1) in, is the complex amplitude at time τ and frequency f, ; ; 1-3: According to the central limit theorem, the short-time Fourier transform STFT coefficient The distribution converges to the complex-valued Gaussian distribution. After decentralization, the decentralization represents Subtracting its mean simplifies it into a circularly symmetric Gaussian distribution, as shown below: (2) in, represents the covariance matrix of the distribution, where represents the conjugate transpose.
[0007] In a possible implementation, step 2: establishing a random model based on the time-frequency spectrum of the signal and estimating model parameters of the random model includes: 2-1: Change the sequence As the observation sequence of the Hidden Markov Model HMM, ; Hidden state sequence , , there are only two hidden states, Indicates the noise state; represents the impact state, and the hidden state sequence is the parameter of the random model; the joint probability distribution of the random model is as follows: (3) in, is the parameter set of the model, represents the initial probability of the model, , express The transition probability is, , express The emission probability matrix, where ; 2-2: Use the forward-backward recursive formula to calculate the maximum likelihood value of equation (3) and calculate the forward probability of different time windows τ and the backward probability , the formula is as follows: (4) (5) 2-3: Use the forward and backward probability formula to calculate the time window τ as the state The posterior probability The calculation is as follows: (6) 2-4: Estimating the covariance matrix of different states i in the model , the calculation formula is as follows: (7).
[0008] In a possible implementation, step three: constructing a time-varying Wiener filter based on Bayes' theorem, includes: 3-1: The basic goal of signal reconstruction is to extract the noise-free non-stationary signal x(t) from the measured signal y(t) with the additive background noise signal n(t). First, according to the Bayesian theory, the τth observation value is obtained. The posterior probability distribution of is: (8) For time τ and frequency f, the posterior probability of the Fourier coefficients of the non-stationary signal is: (9) in and is the covariance matrix of the observation sequence under different states, which can be calculated by formula (7). According to the central limit theorem, the time-frequency spectrum of the non-stationary signal is It also obeys the complex Gaussian distribution, that is: (10) 3-2: By combining formula (9) and formula (10), the time-frequency spectrum of the non-stationary signal is obtained The mean and the covariance matrix As shown below: (11) The covariance matrix Substitute into the mean In the above example, we can obtain the time-frequency spectrum of the non-stationary signal. The expectations are as follows: (12).
[0009] In a possible implementation, the step 4, obtaining the reconstructed non-steady-state signal by inverse time-frequency transform, includes: Perform inverse short-time Fourier transform to obtain time-domain non-stationary signal x ( t ).
[0010] Compared with the prior art, the present invention has the following beneficial effects: The present disclosure discloses a signal reconstruction method based on a time-varying filter, and a Bayesian spectrum amplitude estimation method, which uses the probability density function of the signal and noise process to capture and describe the frequency variation characteristics of non-stationary signals from the perspective of probability theory. By analyzing the hidden state of the signal spectrum, this method not only reveals the evolution process of the signal spectrum, but also provides useful information on the relationship between spectra. This information plays an important role in improving the accuracy of signal estimation, and helps to overcome the limitations of Wiener filtering in processing non-stationary signals, thereby achieving more accurate signal reconstruction and interference suppression. Compared with the classic Wiener filter, it can be seen that there is an additional hidden state posterior probability sequence in formula (12), which can be regarded as a time-varying Wiener filter. Through Adjustment can effectively make up for the limitations of processing non-steady-state signals, thereby achieving more accurate signal reconstruction and interference suppression.
[0011] Through the verification of case effects, it can be found that the Wiener filter combined with the state posterior probability sequence shows significant advantages in signal reconstruction. Specifically, this filter can reconstruct the signal more effectively because the state posterior probability sequence is closely related to the transient impact state information of the signal. Since the transient impact state reflects the key characteristics of the signal, it provides rich and accurate frequency domain information for the Wiener filter. The effective fusion of this frequency domain information enables the filter to accurately extract and reconstruct the detailed features of the original signal when facing complex interference, thereby significantly improving the quality and accuracy of signal reconstruction. This discovery provides strong support for further optimization of signal processing methods. BRIEF DESCRIPTION OF THE DRAWINGS
[0012] Figure 1 A block diagram of a signal reconstruction method based on a time-varying filter according to an embodiment of the present disclosure is shown.
[0013] Figure 2 A waveform diagram showing a hidden state sequence and a disturbed non-stationary signal according to an embodiment of the present disclosure.
[0014] Figure 3 Waveform diagrams for verifying the analysis effect of a time-varying filter according to an embodiment of the present disclosure are shown, wherein (a) is a waveform diagram of a vibration signal, and (b) is a waveform diagram of a reconstructed periodic signal.
[0015] Figure 4 Waveform diagrams for verifying the analysis effect of a time-varying filter according to another embodiment of the present disclosure are shown, wherein (a) is a waveform diagram of a vibration signal, and (b) is a waveform diagram of a reconstructed periodic signal. DETAILED DESCRIPTION
[0016] Various exemplary embodiments, features and aspects of the present disclosure will be described in detail below with reference to the accompanying drawings. The same reference numerals in the accompanying drawings represent elements with the same or similar functions. Although various aspects of the embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless otherwise specified.
[0017] The word “exemplary” is used exclusively herein to mean “serving as an example, example, or illustration.” Any embodiment described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other embodiments.
[0018] In addition, in order to better illustrate the present disclosure, numerous specific details are given in the following specific embodiments. It should be understood by those skilled in the art that the present disclosure can also be implemented without certain specific details. In some examples, methods, means, components and circuits well known to those skilled in the art are not described in detail in order to highlight the main purpose of the present disclosure.
[0019] Figure 1 A block diagram of a signal reconstruction method based on a time-varying filter according to an embodiment of the present disclosure is shown. Figure 1 As shown, the method includes: Step 1 (S01): performing time-frequency analysis on the disturbed non-stationary signal to obtain a time-frequency spectrum; Step 2 (S02): establishing a random model based on the time-frequency spectrum of the signal, and estimating model parameters of the random model; Step 3 (S03): construct a time-varying Wiener filter based on Bayes' theorem; Step 4 (S04): Obtain a reconstructed non-stationary signal through inverse time-frequency transformation.
[0020] In a possible implementation, the step 1 of performing time-frequency analysis on the disturbed non-steady-state signal to obtain a time-frequency spectrum includes: 1-1: Collecting non-steady-state signals of the target object , where T is the number of time points of a single signal sample; 1-2: Select a window function ω(t) to collect the non-steady-state signal The result of the short-time Fourier transform (STFT) is a time-frequency matrix, in which each column represents the spectrum within a window, and each column represents how a frequency changes over time. The short-time Fourier transform conversion formula is: (1) in, is the complex amplitude at time τ and frequency f, ; ; 1-3: According to the central limit theorem, the short-time Fourier transform STFT (STFT, short-time Fouriertransform) coefficients The distribution converges to the complex-valued Gaussian distribution. After decentralization, the decentralization represents Subtracting its mean simplifies it into a circularly symmetric Gaussian distribution, as shown below: (2) in, represents the covariance matrix of the distribution, where represents the conjugate transpose.
[0021] For example, the collected disturbed non-steady-state signal is subjected to time-frequency spectrum analysis. This embodiment uses short-time Fourier transform SFFT (STFT) for illustration, and other time-frequency transforms are also applicable. The calculation formula is shown in formula (1). In the method, the window width Nw and window shift R of the window function of the short-time Fourier transform STFT need to be specifically selected according to the rotation speed of the vibration signal and the sampling frequency. In this embodiment, the window width Nw=128 and the window shift R=8. After the short-time Fourier transform, the coefficients are obtained. , , used in subsequent random models.
[0022] In a possible implementation, step 2: establishing a random model based on the time-frequency spectrum of the signal and estimating model parameters of the random model includes: 2-1: Change the sequence As the observation sequence of the Hidden Markov Model HMM, ; Hidden state sequence , , there are only two hidden states, Indicates the noise state; represents the impact state, and the hidden state sequence is the parameter of the random model; the joint probability distribution of the random model is as follows: (3) in, is the parameter set of the model, represents the initial probability of the model, , express The transition probability is, , express The emission probability matrix, where ; Figure 2 A waveform diagram showing a hidden state sequence and a disturbed non-stationary signal according to an embodiment of the present disclosure. Figure 2 The hidden state sequence of the signal is shown, where 0 represents the noise state and 1 represents the impact state.
[0023] 2-2: Use the forward-backward recursive formula to calculate the maximum likelihood value of equation (3) and calculate the forward probability of different time windows τ and the backward probability , the formula is as follows: (4) (5) 2-3: Use the forward and backward probability formula to calculate the time window τ as the state The posterior probability The calculation is as follows: (6) 2-4: Estimate the covariance matrix of different states i in the model , the calculation formula is as follows: (7).
[0024] For example, through the forward-backward iteration algorithm, the state posterior probability in the model is obtained Sequence, see formula (6) for details, and under different states The covariance matrix of and , see formula (7) for details.
[0025] In a possible implementation, step three: constructing a time-varying Wiener filter based on Bayes' theorem, includes: 3-1: The basic goal of signal reconstruction is to extract the noise-free non-stationary signal x(t) from the measured signal y(t) with the additive background noise signal n(t). First, according to the Bayesian theory, the τth observation value is obtained. The posterior probability distribution of is: (8) For time τ and frequency f, the posterior probability of the Fourier coefficients of the non-stationary signal is: (9) in and is the covariance matrix of the observation sequence under different states, which can be calculated by formula (7). According to the central limit theorem, the time-frequency spectrum of the non-stationary signal is It also obeys the complex Gaussian distribution, that is: (10) 3-2: By combining formula (9) and formula (10), the time-frequency spectrum of the non-stationary signal is obtained The mean and the covariance matrix As shown below: (11) The covariance matrix Substitute into the mean In the above example, we can obtain the time-frequency spectrum of the non-stationary signal. The expectations are as follows: (12) For example, using Bayes' theorem and combining the posterior probability of the signal state Construct a time-varying Wiener filter, see formula (12) for details.
[0026] In step 4, by Perform inverse short-time Fourier transform to obtain time-domain non-stationary signal x ( t ).
[0027] Figure 3 Waveform diagrams for verifying the analysis effect of a time-varying filter according to an embodiment of the present disclosure are shown, wherein (a) is a waveform diagram of a vibration signal, and (b) is a waveform diagram of a reconstructed periodic signal. Figure 4 The following is a waveform diagram for verifying the analysis effect of a time-varying filter according to another embodiment of the present disclosure, wherein (a) is a waveform diagram of a vibration signal, and (b) is a waveform diagram of a reconstructed periodic signal. Figure 3 and Figure 4 In the figure, the horizontal axis represents time (the unit may be seconds), and the vertical axis represents the amplitude of the signal.
[0028] from Figure 3 or Figure 4 It can be seen that after the vibration signal is reconstructed, a reconstructed periodic signal is obtained, wherein the vibration signal is a disturbed signal, achieving more accurate signal reconstruction and interference suppression.
[0029] The present disclosure discloses a signal reconstruction method based on a time-varying filter, and a Bayesian spectrum amplitude estimation method, which uses the probability density function of the signal and noise process to capture and describe the frequency variation characteristics of non-steady-state signals from the perspective of probability theory. By analyzing the hidden state of the signal spectrum, this method not only reveals the evolution process of the signal spectrum, but also provides useful information on the relationship between spectra. This information plays an important role in improving the accuracy of signal estimation, and helps to overcome the limitations of Wiener filtering in processing non-steady-state signals, thereby achieving more accurate signal reconstruction and interference suppression. Compared with the classic Wiener filter, it can be seen that there is an additional hidden state posterior probability sequence in formula (12), which can be regarded as a time-varying Wiener filter. Through adjustment, it can well compensate for the limitations in processing non-steady-state signals, thereby achieving more accurate signal reconstruction and interference suppression.
[0030] Through the verification of case effects, it can be found that the Wiener filter combined with the state posterior probability sequence shows significant advantages in signal reconstruction. Specifically, this filter can reconstruct the signal more effectively because the state posterior probability sequence is closely related to the transient impact state information of the signal. Since the transient impact state reflects the key characteristics of the signal, it provides rich and accurate frequency domain information for the Wiener filter. The effective fusion of this frequency domain information enables the filter to accurately extract and reconstruct the detailed features of the original signal when facing complex interference, thereby significantly improving the quality and accuracy of signal reconstruction. This discovery provides strong support for further optimization of signal processing methods.
[0031] The embodiments of the present disclosure are introduced in detail above. Specific examples are used in this article to illustrate the principles and implementation methods of the present disclosure. The description of the above embodiments is only used to help understand the method of the present disclosure and its core idea. At the same time, for those skilled in the art, according to the idea of the present disclosure, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present disclosure.
[0032] Various aspects of the present disclosure are described herein with reference to flowcharts and / or block diagrams of methods, devices (systems) and computer program products according to embodiments of the present disclosure. It should be understood that each box in the flowchart and / or block diagram and the combination of boxes in the flowchart and / or block diagram can be implemented by computer-readable program instructions.
[0033] The flow chart and block diagram in the accompanying drawings show the possible architecture, function and operation of the system, method and computer program product according to multiple embodiments of the present disclosure. In this regard, each square box in the flow chart or block diagram can represent a part of a module, program segment or instruction, and a part of the module, program segment or instruction includes one or more executable instructions for realizing the specified logical function. In some alternative implementations, the function marked in the square box can also occur in a sequence different from that marked in the accompanying drawings. For example, two continuous square boxes can actually be executed substantially in parallel, and they can sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each square box in the block diagram and / or flow chart, and the combination of the square boxes in the block diagram and / or flow chart can be implemented with a dedicated hardware-based system that performs the specified function or action, or can be implemented with a combination of special hardware and computer instructions.
[0034] The embodiments of the present disclosure have been described above, and the above description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and changes will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The selection of terms used herein is intended to best explain the principles of the embodiments, practical applications, or technical improvements in the market, or to enable other persons of ordinary skill in the art to understand the embodiments disclosed herein.
Claims
1. A signal reconstruction method based on a time-varying filter, characterized in that: The method comprises: Step 1: Perform time-frequency analysis on the disturbed non-stationary signal to obtain the time-frequency spectrum; Step 2: Establish a random model based on the time-frequency spectrum of the signal and estimate the model parameters of the random model; Step 3: Construct a time-varying Wiener filter based on Bayes' theorem; Step 4: Obtain the reconstructed non-stationary signal through inverse time-frequency transform.
2. The signal reconstruction method based on a time-varying filter according to claim 1, characterized in that: The step 1, performing time-frequency analysis on the disturbed non-steady-state signal to obtain a time-frequency spectrum, comprises: 1-1: Collecting non-steady-state signals of the target object , where T is the number of time points of a single signal sample; 1-2: Select a window function ω(t) to collect the non-steady-state signal The result of the short-time Fourier transform (STFT) is a time-frequency matrix, in which each column represents the spectrum within a window, and each column represents how a frequency changes over time. The short-time Fourier transform conversion formula is: （1） in, is the complex amplitude at time τ and frequency f, ; ; 1-3: According to the central limit theorem, the short-time Fourier transform STFT coefficient The distribution converges to the complex-valued Gaussian distribution. After decentralization, the decentralization represents Subtracting its mean simplifies it into a circularly symmetric Gaussian distribution, as shown below: （2） in, represents the covariance matrix of the distribution, where represents the conjugate transpose.
3. The signal reconstruction method based on a time-varying filter according to claim 1, characterized in that: Step 2: Establish a random model based on the time-frequency spectrum of the signal and estimate the model parameters of the random model, including: 2-1: Change the sequence As the observation sequence of the Hidden Markov Model HMM, ; Hidden state sequence , , there are only two hidden states, Indicates the noise state; represents the impact state, and the hidden state sequence is the parameter of the random model; the joint probability distribution of the random model is as follows: （3） in, is the parameter set of the model, represents the initial probability of the model, , express The transition probability is, , express The emission probability matrix, where ; 2-2: Use the forward-backward recursive formula to calculate the maximum likelihood value of equation (3) and calculate the forward probability of different time windows τ and the backward probability , the formula is as follows: （4） （5） 2-3: Use the forward and backward probability formula to calculate the time window τ as the state The posterior probability The calculation is as follows: （6） 2-4: Estimating the covariance matrix of different states i in the model , the calculation formula is as follows: （7）。 4. The signal reconstruction method based on a time-varying filter according to claim 1, characterized in that: Step 3: Construct a time-varying Wiener filter based on Bayes' theorem, including: 3-1: The basic goal of signal reconstruction is to extract the noise-free non-stationary signal x(t) from the measured signal y(t) with the additive background noise signal n(t). First, according to the Bayesian theory, the τth observation value is obtained. The posterior probability distribution of is: （8） For time τ and frequency f, the posterior probability of the Fourier coefficients of the non-stationary signal is: （9） in and is the covariance matrix of the observation sequence under different states, which can be calculated by formula (7). According to the central limit theorem, the time-frequency spectrum of the non-stationary signal is It also obeys the complex Gaussian distribution, that is: （10） 3-2: By combining formula (9) and formula (10), the time-frequency spectrum of the non-stationary signal is obtained The mean and the covariance matrix As shown below: （11） The covariance matrix Substitute into the mean In the above example, we can obtain the time-frequency spectrum of the non-stationary signal. The expectations are as follows: （12）。 5. The signal reconstruction method based on time-varying filter according to claim 1, characterized in that: The fourth step, obtaining the reconstructed non-steady-state signal by inverse time-frequency transform, comprises: Perform inverse short-time Fourier transform to obtain time-domain non-stationary signal x ( t ).