A signal denoising method based on wavelet threshold transform and wiener filtering

Abstract

This invention discloses a signal denoising method based on wavelet threshold transform and Wiener filtering. The method involves obtaining a desired target signal A and a noisy signal B; performing wavelet threshold denoising preprocessing on the noisy signal B; performing discrete wavelet transforms on both the target signal A (the desired signal) and the wavelet threshold-denoised signal C to extract approximate and detail components of each signal segment; constructing a Wiener-Hoff equation using the detail components of signals A and C; and performing Wiener filtering on the detail components of the wavelet threshold-denoised signal C; performing an inverse wavelet transform on the above signal processing results to obtain the denoised signal D; and finally, subtracting the noisy signal B from the denoised signal D to obtain the desired denoised signal E. This invention maintains the linear phase of the signal and outperforms individual Wiener filtering and wavelet threshold denoising algorithms, making it suitable for vibration signal processing.

Description

Technical Field

[0001] This invention belongs to the field of signal processing, specifically relating to a signal denoising method based on wavelet threshold transformation and Wiener filtering. Background Technology

[0002] Bearings are indispensable in the operation of large chemical machinery, especially in reducer equipment. The bearing operating environment is enclosed, highly corrosive, and high-temperature, making it difficult for workers to effectively monitor the bearings while the reducer is running. Therefore, in fault diagnosis, it is usually necessary to analyze the actual measured vibration signals using digital signal processing methods for parameter checking and quality assessment. However, vibration signals inevitably become contaminated with noise during acquisition and transmission, such as white noise caused by thermal vibration. The signal filtering process needs to achieve good noise reduction while ensuring the balanced phase of the vibration signal to enable condition detection and fault diagnosis based on its characteristics.

[0003] In real-world operating environments, the acquired rolling bearing fault characteristic signals are mostly non-stationary sequences, inevitably containing significant noise that masks the original fault characteristics. To accurately acquire rolling bearing fault characteristic signals, reduce noise, and improve the signal-to-noise ratio, data denoising preprocessing is necessary. Furthermore, the selected data denoising method should be combined with subsequent feature extraction and recognition for a more effective approach. Common data preprocessing methods include wavelet thresholding, Empirical Mode Decomposition (EMD), Singular Value Decomposition (SVD), and filtering denoising. Expert diagnosis requires substantial manual labor, while traditional infinite impulse response (IRD) and finite impulse response (FTR) filters struggle to balance linear phase and filtering effectiveness. The classic Wiener filter also fails to achieve the desired results for processing non-stationary vibration signals.

[0004] Therefore, to address the issues of sensitive phase and filtering effect in signal filtering, a signal denoising method based on wavelet threshold transform and Wiener filtering is proposed. This method applies Wiener filtering to the wavelet domain for filtering, achieving filtering requirements and linear phase while minimizing data loss. Summary of the Invention

[0005] Objective of the Invention: To address the problems mentioned in the background art, this invention discloses a signal denoising method based on wavelet threshold transformation and Wiener filtering. The method transforms the vibration signal from the time domain to the wavelet domain, reducing its non-stationary characteristics. It utilizes the linear phase characteristic of Wiener filtering to preserve the original initial phase of the signal. The method denoises the acquired dataset using a soft threshold function and an optimal estimator for stationary processes proposed based on minimum mean square error, satisfying filtering requirements and linear phase.

[0006] Technical Solution: This invention discloses a signal denoising method based on wavelet threshold transform and Wiener filtering, specifically including the following steps:

[0007] Step 1: Obtain normal signal dataset A and noisy signal B from a certain dataset, and use normal signal dataset A as the original signal of the desired signal;

[0008] Step 2: Select an appropriate wavelet and wavelet decomposition level for the noisy signal B, and perform wavelet decomposition on the noisy signal B to obtain the low-frequency and high-frequency components of the signal;

[0009] Step 3: Perform thresholding on the different frequency band signals obtained from the decomposition, and use the thresholded signals to reconstruct the signal to obtain the wavelet threshold denoising signal C;

[0010] Step 4: Using Haar wavelet as the wavelet basis, the original signal A and the wavelet threshold denoised signal C, respectively, are subjected to discrete wavelet transform. The low-frequency and high-frequency signals of the original signal A and the wavelet threshold denoised signal C after discrete wavelet transform are extracted as their corresponding approximate components and detail components. The signal is transformed from the time domain to the wavelet domain.

[0011] Step 5: Take the detail components of the original signal A after discrete wavelet transform and the wavelet threshold-denoising signal C as the desired signal s, respectively. cd Noise signal w cd Construct the observation signal x cd Meanwhile, the autocorrelation function of the observed signal and the cross-correlation function between the expected signal and the observed signal are obtained, the Wienerhof equation is constructed, the filter coefficients are obtained, and the detail components of the wavelet threshold denoised signal C are filtered.

[0012] Step 6: Use the inverse wavelet transform function to perform an inverse transform on the detail components of the wavelet threshold-denoised signal C after filtering in Step 5; use the Haar wavelet as the wavelet basis, and perform wavelet reconstruction on the detail components of the wavelet threshold-denoised signal C after filtering in Step 5 and the approximate components of the original signal A after discrete wavelet transform in Step 4 to obtain the signal estimate D. Calculate the mean square error between the estimated value D and the original signal A, which is the input signal and the expected signal, to obtain a measure reflecting the degree of difference between the estimated value and the estimated value.

[0013] Step 7: Obtain the desired denoised signal E by subtracting the noisy signal B from the denoised signal estimate D.

[0014] Furthermore, in step 2, an appropriate wavelet and wavelet decomposition level are selected for the noisy signal, and the noisy signal is decomposed using wavelet decomposition to obtain the low-frequency and high-frequency components of the signal. The specific method is as follows:

[0015] Step 2.1: Select Haar wavelet as the wavelet basis and perform multi-level decomposition with 5 levels; the Haar wavelet is defined as follows:

[0016]

[0017] Step 2.2: Perform wavelet decomposition on the noisy signal B to obtain two parts: low frequency and high frequency. The multi-level decomposition is to divide the low frequency information into frequency bands to obtain the low frequency and high frequency parts. The noisy signal B is decomposed into ca5, cd5, cd4, cd3, cd2, and cd1 through 5-level wavelet decomposition, where ca is the low frequency information and approximate component, and cd is the high frequency and detail component.

[0018] Furthermore, step 3 involves thresholding the decomposed signal using a soft thresholding function, as shown in the following formula:

[0019]

[0020] In the formula, w represents the wavelet coefficients, thr represents the threshold, and w thr These are the estimated values ​​of the wavelet coefficients of the signal being estimated.

[0021] Furthermore, step 3 involves reconstructing the signal using the threshold-processed signal, specifically as follows:

[0022] The wavelet reconstruction process is the complete opposite of the wavelet decomposition process. The wavelet thresholded denoised signal C can be obtained by performing an inverse wavelet transform on the thresholded signal.

[0023] Furthermore, the specific method in step 4 is as follows:

[0024] Step 4.1: Perform first-order decomposition of the original signal A, which is the desired signal, using Haar wavelet as the wavelet basis;

[0025] Step 4.2: Extract the approximate components and detail components of the original signal A, which is the desired signal in Step 4, respectively;

[0026] Step 4.3: Decompose the wavelet-threshold-denoised signal C into a first-order decomposition using Haar wavelets as the wavelet basis;

[0027] Step 4.4: Extract the approximate and detail components of the wavelet threshold denoised signal C from Step 4.3;

[0028] Furthermore, the specific method of step 5 is as follows:

[0029] Step 5.1: Take the detail components of the desired signal as the desired signal s. cd ;

[0030] Step 5.2: Use the detail components of the wavelet threshold-denoising signal as the noise signal w. cd ;

[0031] Step 5.3: Construct the observation signal x according to the Wienerhof equation. cd The observed signal is:

[0032] x (n) =s (n) +w (n)

[0033] In the formula, w represents the noise signal, s represents the desired signal, and x is the observed signal;

[0034] Step 5.4: Construct the desired signal detail components s (n) and observation data x (n) cross-correlation function R xs (n):

[0035] Here we use e (n) To represent the error between the true value and the estimated value:

[0036] e (n) =s(n)-y(n)

[0037] Obviously e (n) Since it is a random variable, the error criterion for Wiener filtering is the minimum mean square error criterion.

[0038] E[e 2 (n)]=E[(s(n)-y(n)) 2 ]

[0039] Let h(n) be physically realizable, i.e., a causal sequence:

[0040] h(n) = 0, when n < 0

[0041] Therefore, the derivation is as follows:

[0042]

[0043]

[0044] In the formula, s represents the desired signal, x is the observed signal, and E[e 2[n] represents e 2 The mathematical expectation of (n), e 2 (n) represents the error criterion of Wiener filtering, x(nm) takes the value of nm positions in the observed signal, and h(m) is the filter coefficient, which is the m-th filter coefficient;

[0045] To minimize the mean square error, we take the partial derivative of the above equation with respect to each h(m), m = 0, 1, ..., and make it equal to zero, thus obtaining:

[0046]

[0047] Right now

[0048]

[0049] Expressing the above equation using the correlation function R, we obtain the discrete form of the Wienerhof equation:

[0050]

[0051] Step 5.5: Construct the observation data x (n) autocorrelation function R xx (n); Based on the cross-correlation function, N linear equations can be obtained, which can be written in matrix form as follows:

[0052]

[0053] Simplified form:

[0054] R xx H=R xs

[0055] Step 5.6: Solve the Wienerhof equations to obtain the optimal filter coefficients h with minimum mean square error. (N-1) As long as R xx If it is non-singular, then H can be calculated:

[0056] H=R xx -1 R xs

[0057] Where H is the matrix of all h;

[0058] Step 5.7: Filter the detail components of the wavelet threshold denoising signal using an FIR filter. The FIR filter formula is as follows:

[0059] .

[0060] Beneficial effects:

[0061] First, the signal denoising method based on wavelet threshold transform and Wiener filtering designed in this invention can be applied to bearing vibration signal denoising. It preserves the linear phase characteristics of the signal while avoiding significant amplitude distortion and information loss. The algorithm can be used in practical vibration signal denoising environments and can perform offline analysis and processing of vibration signals. This invention maintains the linear phase of the signal while outperforming Wiener filtering and wavelet threshold denoising algorithms used individually.

[0062] Secondly, this invention performs wavelet soft-threshold denoising preprocessing on the noisy vibration signal. The Haar wavelet is used as the wavelet basis to transform the vibration signal from the time domain to the wavelet domain, which can significantly reduce the non-stationary random characteristics of the vibration signal. Then, Wiener filtering is applied to the detail components after decomposition of the noisy signal, preserving the approximate components unchanged. This Wiener filtering method overcomes the problem of unsatisfactory denoising results caused by traditional methods, while also providing better suppression of Gaussian white noise.

[0063] Third, this invention uses a fault-free signal as the desired signal and a fault signal as the noisy signal. The two signals are extracted and classified by wavelet transform to construct the Wiener-Hoff equation for Wiener filtering. Finally, the difference between the obtained approximate desired signal and the noisy signal is calculated to obtain a denoised signal that retains relatively complete detail information, which is beneficial for the extraction of signal fault features. Attached Figure Description

[0064] Figure 1 This is a flowchart illustrating a signal denoising method based on wavelet threshold transform and Wiener filtering.

[0065] Figure 2 This is a schematic diagram illustrating the effect of the signal denoising method based on wavelet threshold transform and Wiener filtering proposed in this invention on the processed simulated signal.

[0066] Figure 3 This is a comparison chart showing the difference between the original signal and the effect of a single denoising algorithm.

[0067] Figure 4 This is a comparison chart showing the effects of the original signal and the method of this invention. Detailed Implementation

[0068] The present invention will now be described in further detail with reference to the accompanying drawings.

[0069] See attached document Figure 1 This invention discloses a signal denoising method based on wavelet threshold transform and Wiener filtering, the specific implementation of which includes the following steps:

[0070] Step 1: Obtain the Case Western Reserve University dataset. Obtain the target dataset A under normal conditions and the outer race fault dataset B; use Python to read the raw signal dataset. In terms of data acquisition, this invention uses the US Western Reserve University bearing public dataset, rather than a vibration signal simulation under completely ideal conditions. The data is closer to the vibration signals collected during bearing operation in real-world environments, making it more realistic. The relevant parameters for data acquisition are: a fault-free vibration signal with a sampling frequency of 48kHz and an approximate motor speed of 1730r / min is used as the expected signal; and an outer race fault signal with a sampling frequency of 48kHz and a single-point damage state obtained by EDM at the same speed is used as the noisy signal.

[0071] Step 2: Select an appropriate wavelet and wavelet decomposition level for the noisy signal B, and perform wavelet decomposition on the noisy signal B to obtain the low-frequency and high-frequency signals. Since Wiener is only applicable to stationary signal processing, while actual fault signals do not have stationary random characteristics, the change from the time domain to the wavelet domain can greatly reduce the non-stationary random characteristics of the vibration signal. Therefore, it is necessary to first convert the vibration signal to the wavelet domain.

[0072] Step 2.1: Select the Haar wavelet basis and perform multi-level decomposition with 5 levels. The Haar wavelet is the simplest orthogonal function. Compared with other orthogonal functions, it has the advantages of simple construction and convenient calculation. Its definition is as follows:

[0073]

[0074] Step 2.2: Perform wavelet decomposition on the noisy signal B to obtain low-frequency and high-frequency components. Specifically, if the wavelet decomposition divides the low-frequency information into frequency bands, for example, performing a 5-level wavelet decomposition on the noisy signal B to obtain ca5, cd5, cd4, cd3, cd2, and cd1, where ca represents the low-frequency information and approximate component, and cd represents the high-frequency, detail component; the frequency band range of the wavelet decomposition is related to the sampling frequency. If an N-level decomposition is performed, the range of each frequency band is as follows:

[0075]

[0076] In the above relationship, F s f is the sampling frequency. max F is the maximum frequency of the signal. s =2f max It is derived from the Nyquist sampling theorem.

[0077] Step 3: Threshold the different frequency band signals obtained from the decomposition. A soft thresholding function is used in the experiment, and the formula is as follows:

[0078]

[0079] In the formula, w represents the wavelet coefficients, thr represents the threshold, and w thr These are the estimated values ​​of the wavelet coefficients of the signal being estimated.

[0080] The threshold selection rule is based on the model y = f(t) + e, where e is Gaussian white noise. This invention uses a fixed threshold.

[0081]

[0082] Where, d j (k) represents the k-th wavelet coefficient of the j-th wavelet, σ u，j Let be the noise variance of the j-th layer wavelet.

[0083] Step 4: Reconstruct the signal using the thresholded signal. The wavelet reconstruction process is the reverse of the wavelet decomposition process; an inverse wavelet transform is performed on the thresholded signal.

[0084] Step 5: Separate low-frequency and high-frequency signals. Using Haar wavelets as the wavelet basis, the original signal A (the desired signal) and the wavelet-threshold-denoised signal C are subjected to discrete wavelet transform. The low-frequency and high-frequency signals of the original signal A and the wavelet-threshold-denoised signal C after the discrete wavelet transform are extracted as their corresponding approximate and detail components, respectively. This transforms the signal from the time domain to the wavelet domain, reducing the non-stationary characteristics of the signal while preserving its useful information to a greater extent.

[0085] Step 5.1: Perform a first-order decomposition of the original signal A, which is the desired signal, using Haar wavelets as the wavelet basis.

[0086] Step 5.2: Input signal A into the wavelet decomposition tool and perform a low-pass filter to obtain approximate components.

[0087] Step 5.3: Input the A signal into the wavelet decomposition tool and perform a high-pass filter to obtain the detail components.

[0088] Step 5.4: Decompose the wavelet threshold-denoised signal C into a first-order decomposition using Haar wavelets as the wavelet basis.

[0089] Step 5.5: Input the C signal into the wavelet decomposition tool and perform a low-pass filter to obtain approximate components.

[0090] Step 5.6: Input the C signal into the wavelet decomposition tool and perform a high-pass filter to obtain the detail components.

[0091] Step 6: Use the detail components of the original signal A after discrete wavelet transform and the wavelet threshold-denoised signal C as the desired signal s, respectively. cdNoise signal w cd Construct the observation signal x cd Simultaneously, the autocorrelation function of the observed signal and the cross-correlation function between the expected signal and the observed signal are obtained, the Wienerhof equation is constructed, the filter coefficients are obtained, and the detail components of the wavelet threshold denoising signal are filtered.

[0092] Step 6.1: Take the detail components of the desired signal as the desired signal s. cd .

[0093] Step 6.2: Use the detail components of the wavelet threshold-denoising signal as the noise signal w. cd .

[0094] Step 6.3: Construct the observation signal x according to the Wienerhof equations cd Based on the derivation of the Wienerhof equation, assume the observed signal is:

[0095] x (n) =s (n) +w (n)

[0096] In the formula, w represents the noise signal, s represents the desired signal, and x is the observed signal.

[0097] Step 6.4: Construct the desired signal detail components s (n) and observation data x (n) cross-correlation function R xs (n):

[0098] Here we use e (n) To represent the error between the true value and the estimated value:

[0099] e (n) =s(n)-y(n)

[0100] Obviously e (n) Since it is a random variable, the error criterion for Wiener filtering is the minimum mean square error criterion.

[0101] E[e 2 (n)]=E[(s(n)-y(n)) 2 ]

[0102] Let h(n) be physically realizable, i.e., a causal sequence:

[0103] h(n) = 0, when n < 0

[0104] Therefore, the derivation is as follows:

[0105]

[0106]

[0107] In the formula, s represents the desired signal, x is the observed signal, and E[e 2 [n] represents e 2 The mathematical expectation of (n), e 2 (n) represents the error criterion of the Wiener filter, x(nm) takes the values ​​at nm positions in the observed signal, and h(m) is the filter coefficient, which is the m-th filter coefficient. To minimize the mean square error, the partial derivative of the above equation with respect to each h(m), m = 0, 1, ..., is equal to zero, resulting in:

[0108]

[0109] Right now

[0110]

[0111] Expressing the above equation using the correlation function R, we obtain the discrete form of the Wienerhof equation:

[0112]

[0113] Step 6.5: Construct observation data x (n) autocorrelation function R xx (n).

[0114] Based on the cross-correlation function, we can obtain N linear equations, which can be written in matrix form as follows:

[0115]

[0116] Simplified form:

[0117] R xx H=R xs

[0118] Step 6.6: Construct the 64th order autocorrelation matrix.

[0119] Step 6.7: Construct a cross-correlation vector of order 64.

[0120] Step 6.8: Solve the Wienerhof equations to obtain the optimal filter coefficients h with minimum mean square error. (N-1) The formula is:

[0121]

[0122] Among them, R xx It needs to be a non-singular matrix, where H is a matrix of all h.

[0123] Step 6.9: The input signal is passed through an FIR Wiener filter to filter the detail components of the wavelet threshold denoising signal. The FIR filter formula is as follows:

[0124]

[0125] Step 7: Perform an inverse wavelet transform on the signal processing result above. The wavelet basis uses the Haar wavelet. The filtered detail components and the approximate components of the desired signal are reconstructed using wavelet transform to obtain the signal estimate D. The mean square error (MSE) can be calculated between this estimate and the input desired signal A to obtain a measure of the difference between the estimated and the estimated quantity. The formula for the mean square error (MSE) is as follows:

[0126]

[0127] Step 8: Obtain the desired denoised signal E by subtracting the noisy signal B from the denoised signal D.

[0128] The effects of this invention can be further illustrated by the following simulation.

[0129] Simulation 1 simulates the denoising of a signal in a completely ideal state by adding Gaussian white noise and applying the method of this invention. Simulation 1 is performed using Python software.

[0130] The effect is as follows Figure 2 The vibration signal under perfectly ideal conditions can be expressed as:

[0131]

[0132] Figure 2 The top left corner shows the original, noise-free vibration signal; Figure 2 The top right corner shows a Gaussian white noise signal with a signal-to-noise ratio of 10. Figure 2 The bottom left corner shows the simulated noisy signal after noise interference; Figure 2 The bottom right corner shows the Wiener filtering denoising results based on wavelet threshold transformation using the method of this invention.

[0133] from Figure 2 As can be seen from the figure in the lower right corner, the denoised signal obtained by combining wavelet threshold transformation and Wiener filtering retains the characteristics of the signal and achieves an effective denoising effect.

[0134] The effectiveness of this invention when applied to real signals can be further illustrated by the following experiments.

[0135] Experiment 1 uses the fault-free signal from the Western Reserve University bearing public dataset as the ideal signal and the outer race fault signal as the noisy signal to perform a denoising experiment using the method of this invention. Experiment 1 was conducted using Python software.

[0136] like Figure 3The first figure represents the vibration amplitude of the noisy original signal; the second figure represents the difference between the denoised result after applying Wiener filtering alone and the original signal; the third figure represents the difference between the denoised result after applying wavelet thresholding alone and the original signal. As shown in the figures, although the single signal preprocessing result has a denoising effect, the denoising effect of using the Wiener filtering algorithm alone is not significant. When using the wavelet thresholding algorithm alone, it can be seen from the figure that the difference is high in areas where the vibration amplitude of the original signal is large, so it cannot guarantee the integrity of the fault feature signal and the components contained in the removed noise signal; the fourth figure represents the difference between the denoised signal and the original signal after using the method of the present invention. It can be seen from the figure that the denoising effect achieved by using the method of the present invention is very close to the desired signal.

[0137] And through the method of the present invention, such as Figure 4 The black line represents the vibration amplitude of the original signal, and the light-colored line represents the signal finally obtained in the experiment; it can be clearly seen that it contains a relatively complete fault characteristic signal, and the signal retains relatively complete detailed information.

[0138] The three algorithms above were analyzed and compared, and the mean square error of the filtered result of each algorithm compared with the original signal was calculated. The data obtained are shown in Table 1.

[0139]

[0140] From a quantitative analysis perspective, the mean square error of the wavelet domain Wiener filtering algorithm (this invention) is smaller than that of Wiener filtering and wavelet threshold filtering, and its performance is also better than that of individual algorithms. Therefore, this algorithm has practical application value.

[0141] The above embodiments are only for illustrating the technical concept and features of the present invention, and their purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly.

Claims

1. A signal denoising method based on wavelet threshold transform and Wiener filtering, characterized in that, Specifically, the steps include the following: Step 1: Obtain normal signal dataset A and noisy signal B from a certain dataset, and use normal signal dataset A as the original signal of the desired signal; Step 2: Select an appropriate wavelet and wavelet decomposition level for the noisy signal B, and perform wavelet decomposition on the noisy signal B to obtain the low-frequency and high-frequency components of the signal; Step 3: Perform thresholding on the different frequency band signals obtained from the decomposition, and use the thresholded signals to reconstruct the signal to obtain the wavelet threshold denoising signal C; Step 4: Using Haar wavelet as the wavelet basis, the original signal A and the wavelet threshold denoised signal C, respectively, are subjected to discrete wavelet transform. The low-frequency and high-frequency signals of the original signal A and the wavelet threshold denoised signal C after discrete wavelet transform are extracted as their corresponding approximate components and detail components. The signal is transformed from the time domain to the wavelet domain. Step 5: Take the detail components of the original signal A after discrete wavelet transform and the wavelet threshold-denoising signal C as the desired signal s, respectively. cd Noise signal w cd Construct the observation signal x cd Meanwhile, the autocorrelation function of the observed signal and the cross-correlation function between the expected signal and the observed signal are obtained, the Wienerhof equation is constructed, the filter coefficients are obtained, and the detail components of the wavelet threshold denoised signal C are filtered. Step 6: Use the inverse wavelet transform function to perform an inverse transform on the detail components of the wavelet threshold-denoised signal C after filtering in Step 5; use the Haar wavelet as the wavelet basis, and perform wavelet reconstruction on the detail components of the wavelet threshold-denoised signal C after filtering in Step 5 and the approximate components of the original signal A after discrete wavelet transform in Step 4 to obtain the signal estimate D. Calculate the mean square error between the estimated value D and the original signal A, which is the input signal and the expected signal, to obtain a measure reflecting the degree of difference between the estimated value and the estimated value. Step 7: Obtain the desired denoised signal E by subtracting the noisy signal B from the denoised signal estimate D.

2. The signal denoising method based on wavelet threshold transform and Wiener filtering according to claim 1, characterized in that: Step 2 involves selecting an appropriate wavelet and wavelet decomposition level for the noisy signal, and then performing wavelet decomposition on the noisy signal to obtain both low-frequency and high-frequency components. The specific method is as follows: Step 2.1: Select Haar wavelet as the wavelet basis and perform multi-level decomposition with 5 levels; the Haar wavelet is defined as follows: Step 2.2: Perform wavelet decomposition on the noisy signal B to obtain two parts: low frequency and high frequency. The multi-level decomposition is to divide the low frequency information into frequency bands to obtain the low frequency and high frequency parts. The noisy signal B is decomposed into ca5, cd5, cd4, cd3, cd2, and cd1 through 5-level wavelet decomposition, where ca is the low frequency information and approximate component, and cd is the high frequency and detail component.

3. The signal denoising method based on wavelet threshold transform and Wiener filtering according to claim 1, characterized in that: Step 3 involves thresholding the decomposed signal using a soft thresholding function, as shown in the following formula: In the formula, w represents the wavelet coefficients, thr represents the threshold, and w thr These are the estimated values ​​of the wavelet coefficients of the signal being estimated.

4. The signal denoising method based on wavelet threshold transform and Wiener filtering according to claim 3, characterized in that: Step 3 involves reconstructing the signal using the threshold-processed signal. The specific method is as follows: The wavelet reconstruction process is the complete opposite of the wavelet decomposition process. The wavelet thresholded denoised signal C can be obtained by performing an inverse wavelet transform on the thresholded signal.

5. The signal denoising method based on wavelet threshold transform and Wiener filtering according to claim 1, characterized in that: The specific method in step 4 is as follows: Step 4.1: Perform first-order decomposition of the original signal A, which is the desired signal, using Haar wavelet as the wavelet basis; Step 4.2: Extract the approximate components and detail components of the original signal A, which is the desired signal in Step 4, respectively; Step 4.3: Decompose the wavelet-threshold-denoised signal C into a first-order decomposition using Haar wavelets as the wavelet basis; Step 4.4: Extract the approximate and detail components of the wavelet threshold denoised signal C from Step 4.

3.

6. The signal denoising method based on wavelet threshold transform and Wiener filtering according to claim 1, characterized in that: The specific method for step 5 is as follows: Step 5.1: Take the detail components of the desired signal as the desired signal s. cd ; Step 5.2: Use the detail components of the wavelet threshold-denoising signal as the noise signal w. cd ; Step 5.3: Construct the observation signal x according to the Wienerhof equation. cd The observed signal is: x (n) =s (n) +w (n) In the formula, w represents the noise signal, s represents the desired signal, and x is the observed signal; Step 5.4: Construct the desired signal detail components s (n) and observation data x (n) cross-correlation function R xs (n): Here we use e (n) To represent the error between the true value and the estimated value: e (n) =s(n)-y(n) Obviously e (n) Since it is a random variable, the error criterion for Wiener filtering is the minimum mean square error criterion. E[e 2 (n)]=E[(s(n)-y(n)) 2 ] Let h(n) be physically realizable, i.e., a causal sequence: h(n) = 0, when n < 0 Therefore, the derivation is as follows: In the formula, s represents the desired signal, x is the observed signal, and E[e 2 [n] represents e 2 The mathematical expectation of (n), e 2 (n) represents the error criterion of Wiener filtering, x(nm) takes the value of nm positions in the observed signal, and h(m) is the filter coefficient, which is the m-th filter coefficient; To minimize the mean square error, we take the partial derivative of the above equation with respect to each h(m), m = 0, 1, ..., and make it equal to zero, thus obtaining: Right now Expressing the above equation using the correlation function R, we obtain the discrete form of the Wienerhof equation: Step 5.5: Construct the observation data x (n) autocorrelation function R xx (n); Based on the cross-correlation function, N linear equations can be obtained, which can be written in matrix form as follows: Simplified form: R xx H=R xs Step 5.6: Solve the Wienerhof equations to obtain the optimal filter coefficients h with minimum mean square error. (N-1) As long as R xx If it is non-singular, then H can be calculated: H=R xx -1 R xs Where H is the matrix of all h; Step 5.7: Filter the detail components of the wavelet threshold denoising signal using an FIR filter. The FIR filter formula is as follows:

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