A noise suppression and signal extraction method based on synchronous compression operator

Abstract

This invention provides a noise suppression and signal extraction method based on a synchronous compression operator, comprising: Step 1, constructing a synchronous compression operator; Step 2, synchronous compression transformation of the synthesized signal: performing synchronous compression transformation on the received synthesized signal; Step 3, noise suppression: discretizing the synchronous compression transformation coefficients obtained in Step 2, and processing the synchronous compression transformation coefficient matrix using a threshold function to obtain the noise-suppressed synchronous compression transformation coefficients; Step 4, signal filtering and extraction: extracting high-resolution transform domain coefficients corresponding to different signal components using a signal filtering and extraction algorithm; Step 5, signal reconstruction: reconstructing the extracted high-resolution transform domain coefficients using the synthesis operator of the synchronous compression operator to obtain each signal component. The method of this invention can improve the time-frequency resolution and separability of signals, reduce the influence of noise on signals, and realize the automatic extraction of signals from different sources in complex electromagnetic environments.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, and relates to noise suppression and signal extraction, specifically to a noise suppression and signal extraction method based on a synchronous compression operator. Background Technology

[0002] With the widespread application of satellite communication, signal transmission faces increasingly severe electromagnetic interference problems. When satellite signals propagate in open wireless environments, they are easily affected by noise from multiple transmission sources, especially in wide-beam environments such as the L-band and S-band. Receivers not only receive valid signals from ground stations and user terminals but may also be affected by various interference sources such as ground base stations and radar. These interference sources can degrade signal quality and affect communication performance. Therefore, effectively reducing the impact of noise and extracting valid signals from multiple signals has become a key technical problem in solving noise suppression and signal extraction in satellite communication.

[0003] To address these issues, transform domain methods have become a research hotspot in signal processing in recent years, particularly in noise suppression and signal separation. Traditional noise suppression methods primarily rely on time-domain and frequency-domain processing techniques, but these methods have limitations. For example, Fourier transform and windowed Fourier transform provide a global view of the signal in the frequency domain but cannot handle local temporal variations, thus lacking in time-frequency resolution. While wavelet transform can provide multi-resolution analysis in the time-frequency domain, it is still limited by the uncertainty principle in some applications, preventing the simultaneous attainment of high time and high frequency resolution. Although nonlinear transforms such as the Wigner-Ville distribution and Cohen-class distribution have made breakthroughs in improving time-frequency resolution, the problem of cross-term interference remains unresolved. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the present invention aims to provide a noise suppression and signal extraction method based on a synchronous compression operator, thereby solving the technical problem that the anti-interference capability and signal quality in satellite communication need to be further improved in the existing technology.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution.

[0006] A noise suppression and signal extraction method based on a synchronous compression operator, the method comprising the following steps.

[0007] Step 1: Construct a synchronous compression operator.

[0008] Calculating synchronous compression transform coefficients using synchronous compression transform The synchronous compression transform is performed using a normalized wavelet compact frame. Operator representation is performed to obtain the synchronous compression operator.

[0009] The synchronous compression operator is expressed as follows: ; In the formula: This represents a vector composed of discretized signals.

[0010] This represents the composition operator of the synchronous compression operator.

[0011] The analytical operator representing the synchronous compression operator.

[0012] Step 2: Synchronous compression and transformation of the synthesized signal.

[0013] The received synthesized signal is analyzed using the synchronous compression operator constructed in step one. A synchronous compression transform is performed to map the synthesized signal from the time domain to the high-resolution time-frequency domain, thereby obtaining the high-resolution transform domain coefficients corresponding to the synthesized signal. ,Right now .

[0014] Step 3, noise suppression.

[0015] The high-resolution transform domain coefficients obtained in step two Discretization is performed to obtain the high-resolution transform domain coefficient matrix. In synchronous compression of the high-resolution time-frequency domain, the coefficient matrix of the high-resolution transform domain is... Using a threshold function The noise is suppressed to obtain the high-resolution transform domain coefficients. .

[0016] Step 4: Signal filtering and extraction.

[0017] The high-resolution transform domain coefficients obtained in step three after processing with the percentage soft thresholding strategy. The algorithm filters and extracts high-resolution transform domain coefficients corresponding to different signal components. After filtering out the high-resolution transform domain coefficients corresponding to a signal, the high-resolution transform domain coefficients are set to zero, and the filtering continues until the stopping criterion is met. Through filtering, the high-resolution transform domain coefficients corresponding to each signal component are extracted.

[0018] Step 5: Signal reconstruction.

[0019] The high-resolution transform domain coefficients corresponding to each signal component extracted in step four are synthesized using a synchronous compression operator. The components are recombined and reconstructed to obtain effective signal components.

[0020] Compared with the prior art, the present invention has the following technical effects.

[0021] (I) The method of the present invention introduces a synchronous compression operator to transform the signal to a high-resolution time-frequency domain, thereby improving the resolution and separability of the signal, significantly improving the signal quality, reducing the impact of noise on the signal, and realizing the automatic extraction of signals from different sources.

[0022] (II) The method of this invention can effectively suppress noise and separate and extract signals from different sources, greatly improving the signal transmission quality of satellite communication in complex electromagnetic environments. By introducing this innovative technology, satellite communication can be provided with stronger anti-interference capabilities and higher signal extraction accuracy, which has important research significance and broad application prospects.

[0023] (III) The method of the present invention overcomes the limitations of traditional transform domain methods, such as low resolution, poor signal separation capability and insufficient noise suppression capability. It can achieve efficient separation and anti-interference extraction of multi-source signals in open wireless environments, and significantly improve the signal quality and reliability of communication systems.

[0024] (IV) This invention realizes the automatic separation and noise suppression of multi-source signals in complex electromagnetic environments, significantly improves the signal extraction accuracy and system anti-interference performance, and provides a new technical means for high-reliability signal transmission. Attached Figure Description

[0025] Figure 1 It consists of the time-domain waveform and frequency-domain spectrum of the synthesized signal.

[0026] Figure 2(a) shows the test signal.

[0027] Figure 2(b) shows the results of time-frequency analysis of the test signal using the traditional windowed Fourier transform method.

[0028] Figure 2(c) shows the results of time-frequency analysis of the test signal using the traditional wavelet transform method.

[0029] Figure 2(d) shows the results of the time-frequency analysis of the test signal using the synchronous compression operator of the present invention.

[0030] Figure 3(a) shows the test signal without noise.

[0031] Figure 3(b) shows the result of noise suppression after processing the coefficients of the windowed Fourier transform using a threshold function.

[0032] Figure 3(c) shows the result of noise suppression after processing the wavelet transform coefficients using a threshold function.

[0033] Figure 3(d) shows the result of noise suppression after applying a threshold function to the coefficients of the SST transform.

[0034] Figure 4 It involves filtering and extracting the distribution of two signal components in the transform domain.

[0035] Figure 5 These are the two reconstructed signal components.

[0036] The specific content of the present invention will be further explained in detail below with reference to the embodiments. Detailed Implementation

[0037] It should be noted that, unless otherwise specified, all operators and methods in this invention are known in the prior art.

[0038] Synchrosqueezing Transform (SST), as a novel time-frequency analysis tool, has garnered significant attention in signal processing in recent years. Initially proposed by Daubechies and Maes in acoustic signal analysis, SST was further analyzed in detail by Daubechies et al. in 2011 as a time-frequency analysis tool similar to Empirical Mode Decomposition (EMD). Compared to traditional transform domain methods, SST improves the signal distribution in the time-frequency domain through a synchronous squeezing strategy, enabling more precise localization of the signal's frequency components and achieving higher time-frequency resolution. Due to its excellent clustering and high resolution, SST exhibits significant advantages in noise suppression and signal extraction. By transforming the signal to the time-frequency domain, SST can effectively distinguish different signal components, improve the separation of effective signals, and thus effectively suppress noise interference, enhancing signal extraction accuracy.

[0039] In recent years, signal processing (SST) has achieved application results in various fields such as medical signal analysis, image processing, and sound signal processing. However, in complex electromagnetic environments, how to more effectively combine SST with noise suppression and signal extraction methods to improve the anti-interference capability and signal quality in satellite communications remains a challenging research topic.

[0040] The noise suppression and signal extraction method based on synchronous compression operators of the present invention can also be called the noise suppression and signal extraction method based on high-resolution transform mechanism. The following are specific embodiments of the present invention. It should be noted that the present invention is not limited to the following specific embodiments. All equivalent modifications made based on the technical solutions of this application fall within the protection scope of the present invention.

[0041] Example: This embodiment presents a noise suppression and signal extraction method based on a synchronous compression operator, characterized in that, as Figure 1 As shown, the method includes the following steps.

[0042] Step 1: Construct a synchronous compression operator.

[0043] Calculating synchronous compression transform coefficients using synchronous compression transform The synchronous compression transform is performed using a normalized wavelet compact frame. Operator representation is performed to obtain the synchronous compression operator.

[0044] The synchronous compression operator is represented as ; In the formula: A vector representing the discrete signals; The synthesizer of synchronous compression operators; The analytical operator representing the synchronous compression operator.

[0045] In step one, the method for constructing synchronous compression transformation includes the following steps.

[0046] Step 101: Calculate the continuous wavelet transforms of the signal in the time and frequency domains. .

[0047] ; In the formula: Signals representing the time domain, ; Represents the space of real numbers that are square-integrable; Indicates time; The signal representing the frequency domain is... Fourier transform; Indicates frequency; Indicates the scale factor; Indicates the translation factor; Representing the basic wavelet in the time domain, Indicates its complex conjugate; The basic wavelet in the frequency domain is denoted as Fourier transform of Indicates its complex conjugate 。

[0048] Step 102: To find the frequency components corresponding to the wavelet coefficients, calculate the frequency modulation demodulation frequency. This yields the frequency components corresponding to each wavelet coefficient.

[0049] ; In the formula: Represents the imaginary unit, satisfying .

[0050] Step 103: Obtain synchronous compression transformation.

[0051] Step 10301, demodulate the frequency in the time-scale domain. The compression process involves energy rearrangement, combining coefficients of the same frequency components, and mapping the time-scale plane to the time-frequency plane. .

[0052] Step 10302, for the signal When the fundamental wavelet in the time domain is an analytic wavelet, ; ; In the formula: Indicates signal At any moment The reconstruction result at the location; Indicates the real part; Describing wavelet function The tolerance constant; This represents a frequency domain variable (angular frequency variable).

[0053] Step 10303, synchronous compression transformation is defined as: ; In the formula: This represents the synchronous compression transform coefficients.

[0054] In the time-scale domain, through synchronous compression transformation, all sums and frequencies are... The corresponding wavelet coefficients are combined to compress the energy back to the frequency domain in the time-frequency domain. Location.

[0055] Step 10304: Use synchronous compression transformation to accurately reconstruct the signal.

[0056] The reconstructed formula is ; In the formula: Indicates the real part; Represents the frequency after discretization; The index represents the frequency after discretization.

[0057] In step 103, the synchronous compression transform can rearrange the coefficients of the wavelet transform in the time-scale domain, resulting in a time-frequency distribution with better time-frequency clustering, which improves the time-frequency resolution and facilitates direct time-frequency analysis of the signal.

[0058] In step one, the specific method for constructing the synchronous compression operator includes the following steps.

[0059] Step 104: Construct the synchronous compression operator.

[0060] Step 10401, when the discretized wavelet functions form a compact frame, the signal... The wavelet transform and reconstruction can be written in the following form: , , In the formula: Indicates the frame coefficient; A vector representing the discrete signals; Indicates a tight frame for wavelets; express and The inner product of the two; Indicates the boundaries of the frame (the upper and lower boundaries are equal); This indicates the row number of the matrix element constructed by the wavelet compact index structure; This represents the column number of the matrix element constructed by the wavelet compact index structure.

[0061] Step 10402, let Then the wavelet transform and inverse transform can be written as: , , Right now ; In the formula: This represents a normalized wavelet compact frame; Step 10403, Define the operator From Mapped to Operators, operators Used to measure the frame coefficient Mapped to The signal above, i.e. Define operators For operators The adjoint operator, operator Used to The signal is projected onto the frame coefficient. Above, that is ; In the formula: Represent the space of summable square sequences; N Represent natural numbers; Indicates the frame coefficient; This indicates that the frame coefficient will be used. With frame function The reconstructed signal obtained after linear combination; Operator Acting on signals The frame coefficients obtained later.

[0062] Step 10404, Define the operator From Mapped to Operators, operators Used to convert synchronous compression transform coefficients Frame coefficients obtained by mapping to wavelet transform Define operators For operators The adjoint operator, Used to measure the frame coefficient Mapped to synchronous compression transform coefficients .

[0063] Step 10405, Define the operator From Mapped to Operators, operators Define operators For operators The adjoint operator, operator .

[0064] Step 10406, the operator As a composition operator, the operator As an analysis operator, the synchronous compression operator is obtained. .

[0065] Step 2: Synchronous compression and transformation of the synthesized signal.

[0066] The received synthesized signal is analyzed using the synchronous compression operator constructed in step one. A synchronous compression transform is performed to map the synthesized signal from the time domain to the high-resolution time-frequency domain, thereby obtaining the high-resolution transform domain coefficients corresponding to the synthesized signal. ,Right now .

[0067] In step two, the synthesized signal includes multiple signal components and noise superposition.

[0068] In step two, the synchronous compression transform redistributes the energy of the traditional time-frequency transform result, so that the originally diffused time-frequency energy is refocused near the actual instantaneous frequency of the signal, thereby improving the time-frequency resolution.

[0069] The technical advantages of steps one and two lie in the fact that, thanks to the characteristics of synchronous compression transform, the synthesized signal achieves higher time-frequency resolution in the high-resolution transform domain (time-frequency domain), and the energy of the effective signal can be concentrated in a smaller region, while noise is diffused into a larger energy space, thus effectively suppressing noise. Simultaneously, the energy concentration of different signals is better, improving separability and facilitating signal extraction.

[0070] Step 3, noise suppression: The high-resolution transform domain coefficients obtained in step two Discretization is performed to obtain the high-resolution transform domain coefficient matrix. In synchronous compression of the high-resolution time-frequency domain, the coefficient matrix of the high-resolution transform domain is... Using a threshold function The noise is suppressed to obtain the high-resolution transform domain coefficients. .

[0071] In step three, the threshold function ; In the formula: Represents the high-resolution transform domain coefficients of synchronous compression transform; The threshold parameter represents the soft thresholding function; ; Indicates a percentage threshold; Indicates the row number of an element in the coefficient matrix; This indicates the column index of the coefficient matrix element.

[0072] In step three, the core idea of ​​the percentage threshold method is to dynamically set a percentage threshold based on the channel's signal-to-noise ratio (SNR) and other communication link parameters. This threshold determines the proportion of signal coefficients retained in the transform domain. To adapt to different communication conditions, the percentage threshold can be dynamically adjusted based on communication link parameters such as the SNR. When the SNR is high, a lower percentage can be selected to retain more coefficients; when the SNR is low, a higher percentage can be selected to ensure that more signal components are retained.

[0073] The technical advantage of step three lies in setting an appropriate threshold, dynamically adjusting the threshold according to channel conditions and signal-to-noise ratio, and further improving the noise suppression effect by using the percentage threshold method.

[0074] Step 4: Signal filtering and extraction.

[0075] The high-resolution transform domain coefficients obtained in step three after processing with the percentage soft thresholding strategy. The algorithm filters and extracts high-resolution transform domain coefficients corresponding to different signal components. After filtering out the high-resolution transform domain coefficients corresponding to a signal, the high-resolution transform domain coefficients are set to zero, and the filtering continues until the stopping criterion is met. Through filtering, the high-resolution transform domain coefficients corresponding to each signal component are extracted.

[0076] Step four, the signal filtering and extraction algorithm includes the following steps.

[0077] Step 40101: Discretize the high-resolution transform domain coefficients.

[0078] The high-resolution transform domain coefficients obtained in step three after processing with the percentage soft thresholding strategy. Discretize the time variable. and frequency variables Discretize them separately, let Then the discretized frequency set is represented as The discretized high-resolution transform domain coefficients are expressed as follows: ; In the formula: Represents the discrete first... Each time sampling point; Indicates the start time; Indicates the time sampling interval; Indicates the discrete-time sequence number; Indicates the first A discrete frequency; Indicates the discrete frequency index.

[0079] Step 40102, the curve corresponding to the coefficients of the signal in the high-resolution transform domain. extract.

[0080] Define the normalized energy of synchronous compression transform. ,pass The optimization equation is obtained, and the optimal frequency position at different time points is extracted by solving the optimization equation. At different times The curves corresponding to the coefficients of the constituent signal in the high-resolution transform domain For each point in time The frequency search range is limited to In the formula, Indicates a point in time The corresponding local frequency search interval, This indicates the width of the frequency window, used to control the frequency resolution range.

[0081] Normalized energy of synchronous compression transform ; The optimization equation is ; In the formula: This represents the discrete frequency trajectory of the signal in the transform domain. ; Indicates a point in time The corresponding frequency position in the transform domain; This represents the optimal frequency position that satisfies the optimization equation; This represents the number of discrete-time sampling points; Indicates discrete frequency intervals; This represents the regularization parameter, used to control the smoothness of the extracted curve; Indicates the time sequence number of the discretization; This represents the normalized energy of the synchronous compression transformation.

[0082] Step 40103: Obtain the high-resolution transform domain coefficients corresponding to the signal components.

[0083] Based on the curve corresponding to the coefficients of the signal in the high-resolution transform domain The first signal component is obtained. Corresponding high-resolution transform domain coefficients ;make Continuing to solve the optimization equations, we obtain the curve corresponding to the second signal component and the high-resolution transform domain coefficients, and so on.

[0084] In step four, the stopping criteria are as follows: if the number of signals is known, the filtering stops after reaching the predetermined number of signals to be filtered; if the number of signals is unknown, a stopping criterion based on coefficient variance is adopted, and the filtering process stops when the variance of the high-resolution transform domain coefficients is lower than the threshold.

[0085] In this embodiment, if the number of signals is known, the filtering process can determine when to stop filtering based on a preset number of signal sources. The specific steps are as follows.

[0086] Step 40201: During each filtering, extract a signal component from the high-resolution transform domain coefficients.

[0087] Step 40202: Record the number of signals extracted. .

[0088] Step 40203: Determine whether the current number of signals has reached the predetermined number of signal sources. If the target number is reached, the filtering process will stop. The filtering process will automatically stop when the number of filtered signals reaches the set number of signal sources.

[0089] In this embodiment, if the number of signals is unknown, a stopping criterion based on the variance of the transform coefficients is used. Specifically, the variance of the transform coefficients is calculated, and the variance value is used to determine whether the signal source has been completely extracted. Generally, as the screening process progresses, the remaining signal components gradually become smaller, eventually reaching a very low variance. In this method, the variance of the transform coefficients is used to measure the degree of residual signal after screening. The smaller the variance, the less energy of the remaining signal, and the screening process can be stopped earlier. The specific steps are as follows.

[0090] Step 40301: Calculate the variance of the high-resolution transform domain coefficients.

[0091] High-resolution transform domain coefficients variance The calculation formula is: ; ; In the formula: This indicates the number of frequency indices, i.e. Quantity; This indicates the number of time indexes, i.e. Quantity; This indicates the total number of coefficients. ; This represents the mean of all high-resolution transform domain coefficients; Step 40302: Determine the variance threshold.

[0092] Variance threshold This is used to determine whether the signal is sufficiently sparse. The specific setting method is as follows.

[0093] In the initial stage, it is assumed that the main component of the signal accounts for most of the energy, so the initial variance is large.

[0094] As the screening process continues, the energy of the remaining signals gradually decreases, and the variance gradually decreases.

[0095] The variance threshold can be set based on experience or dynamically adjusted using parameters such as signal-to-noise ratio (SNR). Generally, when the variance is below the set threshold, the screening process can stop, meaning that the signal has been fully extracted and the remaining part is mainly noise.

[0096] The formula for setting the variance threshold is as follows: ; In the formula: This represents an empirical coefficient, typically ranging from 0.1 to 0.5.

[0097] This represents the variance of the transformation coefficients in the initial stage, calculated during the first screening.

[0098] Step 40303: Stop criterion determination.

[0099] When the calculated variance of the transformation coefficients Less than the preset variance threshold Stop the screening process when the time comes.

[0100] Step 5: Signal reconstruction.

[0101] The high-resolution transform domain coefficients corresponding to each signal component extracted in step four are synthesized using a synchronous compression operator. The components are recombined and reconstructed to obtain effective signal components.

[0102] In step five, the method of recombining and reconstructing the synthesis operators using synchronous compression operators is as follows: ; In the formula: Represents the discretized The vector formed; This indicates the selected first... One signal component; Indicates time; The synthesizer of synchronous compression operators; The high-resolution transform domain coefficients after discretization The matrix formed; This indicates the selected first... Each signal component The corresponding high-resolution transform domain coefficients; Indicates a point in time The corresponding local frequency search interval; Indicates the current moment; Indicates the time sequence number of the discretization.

[0103] Application example: This application example provides a noise suppression and signal extraction method based on the synchronous compression operator in the above embodiments. The method includes the following steps.

[0104] Step 1: Construct a synchronous compression operator.

[0105] Calculating synchronous compression transform coefficients using synchronous compression transform The synchronous compression transform is performed using a normalized wavelet compact frame. Operator representation is performed to obtain the synchronous compression operator.

[0106] In this application example, the specific process of step one follows the specific process of step one given in the embodiment.

[0107] Step 2: Synchronous compression and transformation of the synthesized signal.

[0108] The received synthesized signal is analyzed using the synchronous compression operator constructed in step one. A synchronous compression transform is performed to map the synthesized signal from the time domain to the high-resolution time-frequency domain, thereby obtaining the high-resolution transform domain coefficients corresponding to the synthesized signal. ,Right now ; In this application example, the specific process of step two follows the specific process of step two given in the embodiment.

[0109] In this application example, we specifically demonstrate the noise suppression and signal extraction effects based on the synchronous compression operator using synthesized signals, and compare them with commonly used transform domain methods such as windowed Fourier transform and wavelet transform.

[0110] Synthetic signal The time-domain waveform and frequency-domain spectrum are as follows Figure 1 As shown, from Figure 1 It can be seen that the two cannot be separated, whether in the time domain or the frequency domain.

[0111] Using synthesized signals As the test signal, as shown in Figure 2(a), it consists of two signal components and noise: ; ; ; in, This represents Gaussian white noise.

[0112] Next, the synthesized signal is subjected to windowed Fourier transform, wavelet transform, and SST transform, as shown in Figures 2(b) to 2(d). The windowed Fourier transform uses a 128-point Hamming window, the wavelet transform uses the Morlet wavelet, and the SST transform is calculated using the synchronous compression transform definition formula given in step 10303. The operator form expression is as follows: .

[0113] From the time-frequency analysis results shown in Figures 2(b) to 2(d), it is clear that the noise is distributed throughout the energy space of the transform domain, causing blurring of the time-frequency graph. All three transforms can distinguish between two signal components, but the windowed Fourier transform and wavelet transform are affected by the window function or wavelet function, causing the signal energy to diffuse in the transform domain and the energies of the two signal components to overlap. Compared to traditional transform domain tools, the SST transform has better signal concentration and makes it easier to distinguish between two signal components. Furthermore, if the coefficients of the signal in the transform domain are determined, i.e., the energy distribution space corresponding to the signal, only the coefficients corresponding to the signal are retained, and the remaining coefficients are set to zero, noise suppression can be achieved. The SST transform has better concentration, fewer corresponding coefficients, and can filter out more noise.

[0114] Step 3, noise suppression: The high-resolution transform domain coefficients obtained in step two Discretization is performed to obtain the high-resolution transform domain coefficient matrix. In synchronous compression of the high-resolution time-frequency domain, the coefficient matrix of the high-resolution transform domain is... Using a threshold function The noise is suppressed to obtain the high-resolution transform domain coefficients. .

[0115] In this application example, the specific process of step three follows the specific process of step three given in the embodiment.

[0116] In this specific application example, a percentage threshold strategy is used to synthesize the signal. The signal-to-noise ratio is 5dB, and the percentage threshold is 90%. The noise-free test signal is shown in Figure 3(a). The coefficients of the windowed Fourier transform, wavelet transform, and SST transform are processed using threshold functions, and the noise-suppressed results are shown in Figures 3(b) to 3(d). As can be seen from Figures 3(b) to 3(d), compared with the traditional windowed Fourier transform and wavelet transform, the high-resolution transform domain coefficients processed by the percentage soft threshold strategy of this invention are significantly improved. Noise suppression can effectively suppress more noise.

[0117] Step 4: Signal filtering and extraction.

[0118] The high-resolution transform domain coefficients obtained in step three after processing with the percentage soft thresholding strategy. The algorithm filters and extracts high-resolution transform domain coefficients corresponding to different signal components. After filtering out the high-resolution transform domain coefficients corresponding to a signal, the high-resolution transform domain coefficients are set to zero, and the filtering continues until the stopping criterion is met. Through filtering, the high-resolution transform domain coefficients corresponding to each signal component are extracted.

[0119] In this application example, the specific process of step four follows the specific process of step four given in the embodiment.

[0120] In this specific application example, since the number of signal sources is known, the filtering process automatically stops when the number of filtered signals reaches the set number of signal sources, according to the stopping criterion. Figure 4 The transform domain distribution corresponding to the two signal components that have been filtered and extracted is the high-resolution transform domain coefficient.

[0121] Step 5: Signal reconstruction.

[0122] The high-resolution transform domain coefficients corresponding to each signal component extracted in step four are synthesized using a synchronous compression operator. The components are recombined and reconstructed to obtain effective signal components.

[0123] In this application example, step five follows the specific process of step five given in the embodiment.

[0124] In this application example, the two reconstructed signal components are as follows: Figure 5 As shown.

[0125] As can be seen from this application example, by adopting a percentage soft threshold strategy in the high-resolution transform domain, dynamic adaptive noise suppression is achieved, which effectively preserves the main signal energy and significantly reduces background noise. Subsequently, by combining an adaptive signal filtering algorithm based on optimization problem solving with a stopping criterion, automatic separation and accurate extraction of multi-source signals are completed.

Claims

1. A method for noise suppression and signal extraction based on a synchronous compression operator, characterized in that, The method includes the following steps: Step 1: Construct the synchronous compression operator: Calculating synchronous compression transform coefficients using synchronous compression transform The synchronous compression transform is performed using a normalized wavelet compact frame. Operator representation is performed to obtain the synchronous compression operator; The synchronous compression operator is expressed as follows: ; In the formula: A vector representing the discrete signals; The synthesizer of synchronous compression operators; The analytical operator representing the synchronous compression operator; Step 2, Synchronous Compression Transformation of Synthetic Signal: The received synthesized signal is analyzed using the synchronous compression operator constructed in step one. A synchronous compression transform is performed to map the synthesized signal from the time domain to the high-resolution time-frequency domain, thereby obtaining the high-resolution transform domain coefficients corresponding to the synthesized signal. ,Right now ; Step 3, noise suppression: The high-resolution transform domain coefficients obtained in step two Discretization is performed to obtain the high-resolution transform domain coefficient matrix. In synchronous compression of the high-resolution time-frequency domain, the coefficient matrix of the high-resolution transform domain is... Using a threshold function The noise is suppressed to obtain the high-resolution transform domain coefficients. ; Step 4, Signal Filtering and Extraction: The high-resolution transform domain coefficients obtained in step three after processing with the percentage soft thresholding strategy. The high-resolution transform domain coefficients corresponding to different signal components are selected through signal filtering and extraction algorithms. After selecting the high-resolution transform domain coefficients corresponding to a signal, the high-resolution transform domain coefficients are set to zero, and the selection of the high-resolution transform domain coefficients corresponding to the next signal is continued until the stopping criterion is met. Through filtering, the high-resolution transform domain coefficients corresponding to each signal component are extracted. Step 5, Signal Reconstruction: The high-resolution transform domain coefficients corresponding to each signal component extracted in step four are synthesized using a synchronous compression operator. The components are recombined and reconstructed to obtain effective signal components.

2. The noise suppression and signal extraction method based on synchronous compression operators as described in claim 1, characterized in that, Step one, the method for constructing the synchronous compression transformation includes the following steps: Step 101: Calculate the continuous wavelet transforms of the signal in the time and frequency domains. : ； In the formula: Signals representing the time domain, ; Represents the space of real numbers that are square-integrable; Indicates time; The signal representing the frequency domain is... Fourier transform; Indicates frequency; Indicates the scale factor; Indicates the translation factor; Representing the basic wavelet in the time domain, Indicates its complex conjugate; The basic wavelet in the frequency domain is denoted as Fourier transform of Indicates its complex conjugate; Step 102, calculate the FM demodulation frequency. ; In the formula: Represents the imaginary unit, satisfying ; Step 103, obtain synchronous compression transformation: Step 10301, demodulate the frequency in the time-scale domain. The compression process involves energy rearrangement, combining coefficients of the same frequency components, and mapping the time-scale plane to the time-frequency plane. ; Step 10302, for the signal When the fundamental wavelet in the time domain is an analytic wavelet, ; ; In the formula: Indicates signal At any moment The reconstruction result at the location; Indicates the real part; Describing wavelet function The tolerance constant; Represents frequency domain variables; Step 10303, synchronous compression transformation is defined as: ； In the formula: Indicates the synchronous compression transform coefficients; In the time-scale domain, through synchronous compression transformation, all sums and frequencies are... The corresponding wavelet coefficients are combined to compress the energy back to the frequency domain in the time-frequency domain. Location; Step 10304: Accurate reconstruction of the signal is performed using synchronous compression transformation; The formula for reconstruction is: ; In the formula: Indicates the real part; Represents the frequency after discretization; The index represents the frequency after discretization.

3. The noise suppression and signal extraction method based on synchronous compression operators as described in claim 1, characterized in that, Step one involves the following steps to construct the synchronous compression operator: Step 104, Construct the synchronous compression operator: Step 10401, when the discretized wavelet functions form a compact frame, the signal... The wavelet transform and reconstruction can be written in the following form: ， ， In the formula: Indicates the frame coefficient; A vector representing the discrete signals; Indicates a tight frame for wavelets; express and The inner product of the two; Indicates the boundaries of the frame (the upper and lower boundaries are equal); This indicates the row number of the matrix element constructed by the wavelet compact index structure; Represents the column index of the matrix element constructed by the wavelet compact index structure; Step 10402, let Then the wavelet transform and inverse transform can be written as: , ， Right now ; In the formula: This represents a normalized wavelet compact frame; Step 10403, Define the operator From Mapped to Operators, operators Used to measure the frame coefficient Mapped to The signal above, i.e. Define operators For operators The adjoint operator, operator Used to The signal is projected onto the frame coefficient. Above, that is ; In the formula: Represents the space of summable square sequences; N Represent natural numbers; Indicates the frame coefficient; This indicates that the frame coefficient will be used. With frame function The reconstructed signal obtained after linear combination; Operator Acting on signals The resulting frame coefficients; Step 10404, Define the operator From Mapped to Operators, operators Used to compress transform coefficients Frame coefficients obtained by mapping to wavelet transform Define operators For operators The adjoint operator, Used to measure the frame coefficient Mapped to synchronous compression transform coefficients ; Step 10405, Define the operator From Mapped to Operators, operators Define operators For operators The adjoint operator, operator ; Step 10406, the operator As a composition operator, the operator As an analysis operator, the synchronous compression operator is obtained. .

4. The noise suppression and signal extraction method based on synchronous compression operators as described in claim 1, characterized in that, In step three, the threshold function ; In the formula: Represents the high-resolution transform domain coefficients of synchronous compression transform; The threshold parameter representing the soft thresholding function is determined by the maximum value of the high-resolution transform domain coefficients and the percentage threshold. Together, they are used to suppress small-amplitude coefficients in the transform domain, thereby achieving noise suppression; ; Indicates a percentage threshold; Indicates the row number of an element in the coefficient matrix; This indicates the column index of the coefficient matrix element.

5. The noise suppression and signal extraction method based on synchronous compression operators as described in claim 1, characterized in that, Step four, the signal filtering and extraction algorithm includes the following steps: Step 40101, High-resolution transform domain coefficient discretization: The high-resolution transform domain coefficients obtained in step three, processed using the percentage soft thresholding strategy. Discretize the time variable. and frequency variables Discretize them separately, let Then the discretized frequency set is represented as The discretized high-resolution transform domain coefficients are expressed as follows: ; In the formula: Represents the discrete first... Each time sampling point; Indicates the start time; Indicates the time sampling interval; Indicates the discrete-time sequence number; Indicates the first A discrete frequency; Indicates the discrete frequency index; Step 40102, the curve corresponding to the coefficients of the signal in the high-resolution transform domain. extract: Define the normalized energy of synchronous compression transform ,pass The optimization equation is obtained, and the optimal frequency position at different time points is extracted by solving the optimization equation. At different times The curves corresponding to the coefficients of the constituent signal in the high-resolution transform domain ; For each time point The frequency search range is limited to: in: Indicates a point in time The corresponding local frequency search interval; Indicates the width of the frequency window, used to control the frequency resolution range; The normalized energy of the synchronous compression transformation ; The optimization equation is as follows: ; In the formula: Represents the discrete frequency trajectory of a signal in the transform domain; Indicates a point in time The corresponding frequency position in the transform domain; This represents the optimal frequency position that satisfies the optimization equation; This represents the number of discrete-time sampling points; Indicates discrete frequency intervals; This represents the regularization parameter, used to control the smoothness of the extracted curve; Step 40103: Obtain the high-resolution transform domain coefficients corresponding to the signal components. Based on the curve corresponding to the coefficients of the signal in the high-resolution transform domain The first signal component is obtained. Corresponding high-resolution transform domain coefficients ;make Continuing to solve the optimization equations, we obtain the curve corresponding to the second signal component and the high-resolution transform domain coefficients, and so on.

6. The noise suppression and signal extraction method based on synchronous compression operators as described in claim 1, characterized in that, In step four, the stopping criterion is as follows: if the number of signals is known, the filtering stops after reaching the predetermined number of signals to be filtered; if the number of signals is unknown, a stopping criterion based on coefficient variance is adopted, and the filtering process stops when the variance of the high-resolution transform domain coefficients is lower than the threshold.

7. The noise suppression and signal extraction method based on synchronous compression operators as described in claim 1, characterized in that, In step five, the method of recombining and reconstructing the synthesis operators using synchronous compression operators is as follows: ; In the formula: Represents the discretized The vector formed; This indicates the selected first... One signal component; Indicates time; The synthesizer of synchronous compression operators; The high-resolution transform domain coefficients after discretization The matrix formed; This indicates the selected first... Each signal component The corresponding high-resolution transform domain coefficients; Indicates a point in time The corresponding local frequency search interval; Represents the discrete first... Each time sampling point; Indicates the time sequence number of the discretization.

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