Non-stationary signal decomposition method based on adaptive frequency scanning demodulation

Abstract

The invention discloses a non-stationary signal decomposition method based on adaptive frequency scanning demodulation, and belongs to the technical field of signal processing. The method is suitable for component extraction and analysis of complex noise-containing and multi-component non-stationary signals. The method comprises five steps of accurate frequency locking, synchronous demodulation, intelligent bandwidth judgment, low-pass filtering extraction and remodulation recovery. Firstly, the accurate center frequency of a target component is locked through frequency domain analysis and optimization search, then a target signal is down-converted to a base band by using an orthogonal carrier, and the required filtering bandwidth is intelligently judged according to the energy distribution of the base band. And then, a Gaussian low-pass filter is adopted to extract a target mode on a baseband, and finally, the signal is re-modulated to the original frequency and amplitude correction is carried out. According to the method, high-resolution decomposition of signals in a non-stationary, multi-component and strong-noise environment is realized, and the method has the advantages of high adaptability, high resolution, excellent anti-noise performance and the like, and can meet complex signal processing requirements in multiple fields.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, and more specifically relates to a method for decomposing nonstationary signals based on adaptive frequency scanning demodulation. Background Technology

[0002] Currently, the analysis and processing of complex nonlinear signals has become a common challenge that many cutting-edge fields, such as signal processing, biomedical engineering, financial time series analysis, and physical system monitoring, urgently need to overcome. Although classical linear methods such as Fourier transform have matured in stationary signal processing, their inherent limitations make it difficult to effectively capture the time-varying dynamics and non-stationary properties of signals. To address this, nonlinear decomposition techniques such as Empirical Mode Decomposition (EMD) and its improved algorithms, wavelet transform, and blind source separation have emerged and are gradually becoming more widespread in engineering practice. However, when dealing with increasingly complex scenarios, real-world problems such as strong noise interference, multi-component aliasing, instantaneous frequency jumps, and increased non-stationarity have made the deep-seated shortcomings of existing methods increasingly apparent.

[0003] First, the theoretical foundation and stability of adaptive decomposition techniques remain weak. While mode decomposition, represented by EMD, possesses excellent adaptive capabilities, its mathematical basis is not rigorous enough. The decomposition process is susceptible to endpoint effects and mode aliasing, and it is highly sensitive to noise, easily generating spurious components with ambiguous physical meaning. Even though improved strategies such as Ensemble Empirical Mode Decomposition (EEMD) alleviate some of these shortcomings with the help of noise, they are accompanied by a sharp increase in computational overhead. At the same time, parameter settings rely excessively on prior experience, making it difficult to reliably guarantee the reproducibility and robustness of the algorithm.

[0004] Secondly, traditional time-frequency analysis tools face significant limitations in resolution and flexibility. While wavelet transform can reveal local time-frequency features, its accuracy is constrained by the Heisenberg uncertainty principle, and the pre-defined basis functions significantly affect the results, making it difficult to perfectly match the intrinsic structure of the signal. Faced with drastically changing frequencies or strongly non-stationary signals, wavelet analysis with fixed basis functions struggles to balance time-domain and frequency-domain accuracy, potentially obscuring weak components or generating misleading time-frequency representations.

[0005] Furthermore, existing technologies still need to make breakthroughs in decoupling complex coupled components. Real-world signals often contain multiple highly mixed components in the time and frequency domains, and are frequently accompanied by complex interactions such as nonlinear phase modulation and amplitude coupling. While blind source separation and other methods perform reasonably well under linear mixed conditions, their effectiveness drops sharply when faced with nonlinear coupling scenarios. In addition, their high dependence on statistical independence significantly limits their applicability in systems with intricate physical mechanisms.

[0006] Furthermore, noise resistance and model universality need to be further enhanced. Most decomposition methods experience a sharp performance drop under low signal-to-noise ratio conditions, and the denoising and decomposition stages are often executed separately, easily leading to signal distortion or information loss. At the same time, many algorithms are tailored to specific signal types, lacking a unified analysis architecture and failing to meet diverse decomposition needs such as the coexistence of oscillating and transient signals.

[0007] Finally, computational performance and scalability constitute key obstacles to practical application. With the widespread use of high-dimensional, massive data applications, most iterative decomposition algorithms encounter bottlenecks such as high complexity and large memory consumption, making it difficult to support real-time or near-real-time processing requirements. This severely restricts their deployment and application in embedded platforms and online monitoring scenarios. Summary of the Invention

[0008] This invention is a signal decomposition method based on the principle of phase-locked demodulation. Unlike traditional filter banks or empirical mode decomposition, this invention does not directly segment the signal in the frequency domain. Instead, it uses mathematical methods to "shift" the target frequency component to zero frequency (baseband), processes it in the baseband, and then "shifts" it back.

[0009] To achieve the above objectives, the present invention employs the following technical solution: The method includes the following steps: Precise frequency locking: For noisy signals, the seed frequency is first roughly estimated through frequency domain analysis. Within the preset frequency range, for each candidate frequency, an optimization algorithm is used to search for the precise center frequency that maximizes the low-frequency energy of the signal after complex exponential demodulation. Synchronous demodulation: Based on the obtained precise center frequency, an orthogonal carrier is constructed to downconvert the noisy signal to the baseband, so that the target component becomes a DC component and the interference component is converted into a high-frequency AC term; Intelligent bandwidth determination: Perform spectrum analysis on the baseband signal, extract the energy distribution of DC and its adjacent range, and determine whether it is an amplitude modulation or frequency modulation signal based on the sideband energy ratio. Expand the bandwidth to include the sideband. If it is determined to be an independent single-frequency signal, use an extremely narrow bandwidth method to isolate the target component. Low-pass filter extraction: A Gaussian low-pass filter is applied to the baseband to extract the complex envelope of the target mode. The filter bandwidth is dynamically set according to the intelligent bandwidth determination step. Remodulation recovery: The extracted baseband envelope data is moved back to the original frequency, and the amplitude is corrected by orthogonal projection to finally obtain the target mode signal.

[0010] In one approach, the precise frequency locking specifically includes: Noisy signal is provided Extracting the narrowband components with unknown frequencies First, a seed frequency is roughly estimated using FFT. Construct an optimization problem to find a frequency. This maximizes the low-frequency (DC) energy of the signal after complex exponential demodulation. When the demodulation frequency f is exactly equal to the signal frequency f k Only when a constant term (DC component) appears in the product term will the integral value be maximized; The fminbnd optimization algorithm is used to search over a continuous domain.

[0011] In one scheme, the intelligent bandwidth determination determines the sideband energy ratio by analyzing the energy distribution of the baseband spectrum, and dynamically adjusts the filter bandwidth according to the evaluation results; For baseband signals Perform spectrum analysis Check the energy distribution near 0 Hz: Define the sideband energy ratio R: 1) If (Threshold): Determined to be an amplitude / frequency modulation (AM / FM) signal; indicating the presence of accompanying sidebands near the baseband; Strategy: (Expand bandwidth and accommodate sidebands); 2) If It is determined to be an independent single-frequency signal; Strategy: (Extremely narrow bandwidth, neighboring nodes removed).

[0012] In one scheme, the synchronous demodulation specifically includes: Precise frequency obtained by locking Construct orthogonal carrier signals and downconvert the target component to baseband: Expand signal components: Target component (frequency) ): becomes 0Hz; Interference components (frequency) ):become High-frequency communication items.

[0013] In one approach, the low-pass filtering extraction uses a Gaussian low-pass filter to filter the baseband signal, and the filter bandwidth corresponds to the output of the bandwidth determination step. Application of Gaussian low-pass filters in baseband Extract the complex envelope of the target mode: in ; Extracted baseband modes: .

[0014] In one approach, the remodulation recovery is achieved by correcting the target component amplitude using an orthogonal projection method to counteract error signals introduced during demodulation. The extracted baseband envelope is moved back to the original frequency. : Finally, the amplitude is corrected using orthogonal projection: .

[0015] In one approach, the method can recursively iterate over a multi-component non-stationary signal to extract multiple different frequency components from the signal.

[0016] Beneficial effects of this invention: 1) It transforms the complex bandpass separation problem into a simple baseband lowpass problem. In the baseband, it is very easy to distinguish between 0Hz and 4Hz, which makes it easy to solve the separation problem of 58Hz / 62Hz.

[0017] 2) Software phase-locked loop (PLL): Using fminbnd for frequency locking, the PLL is simulated to simulate a physical PLL amplifier, so that the frequency estimation accuracy is not limited by the FFT fence effect.

[0018] 3) Dynamic bandwidth: By analyzing the characteristics of the demodulated baseband spectrum (whether there are sidebands), it automatically decides whether to "extract wideband" or "extract narrowband", perfectly balancing the integrity of the amplitude-modulated signal and the separation of the near-frequency signal.

[0019] The core advantage of this method lies in transforming the "bandpass filtering" problem into a "lowpass filtering" problem. In the baseband (near 0Hz), we can very easily design filters with bandwidths as narrow as 0.1Hz or even narrower, thereby achieving perfect separation of ultra-near-frequency signals (such as 58Hz / 62Hz), which is difficult to achieve with direct bandpass filtering. Attached Figure Description

[0020] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is the time-domain waveform of the hybrid signal x(t) and its components in this invention; Figure 3 This is the decomposition result of the mixed signal x(t) in this invention; Figure 4 The time-domain waveforms of the hybrid signal sig(t) and its components of this invention are shown. Figure 5This is the decomposition result of the mixed signal sig(t) of the present invention; Figure 6 The simulated signal and its components are those of this invention; Figure 7 This is the decomposition result of the simulation signal in this invention. Detailed Implementation

[0021] To facilitate understanding of the present invention, a more complete description will be given below with reference to the accompanying drawings. Typical embodiments of the invention are shown in the drawings. However, the invention can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete.

[0022] Unless otherwise defined, all technical and scientific terms used in this invention have the same meaning as understood by one of ordinary skill in the art to which this invention pertains. The terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. To facilitate understanding, the invention will now be described more fully with reference to the accompanying drawings. Typical embodiments of the invention are shown in the drawings. However, the invention can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to make the disclosure of the invention more thorough and complete.

[0023] like Figure 1 As shown, a non-stationary signal decomposition method based on adaptive frequency scanning demodulation is implemented as follows: Step 1: Precise frequency locking, with noisy signal included. Extracting the narrowband components with unknown frequencies .

[0024] First, a seed frequency is roughly estimated using FFT. To obtain the accurate center frequency This invention constructs an optimization problem. Its objective is to find a frequency... This maximizes the low-frequency (DC) energy of the signal after complex exponential demodulation. Only when the demodulation frequency f is exactly equal to the signal frequency fk will a constant term (DC component) appear in the product term, and the integral value will be at its maximum.

[0025] The fminbnd optimization algorithm is used to search in a continuous domain, achieving a precision far exceeding that of the FFT resolution.

[0026] Step 2: Synchronous demodulation, using the locked precise frequency Construct orthogonal carrier signals and downconvert the target component to baseband: Expand signal components: Target component (frequency) : becomes 0Hz (DC).

[0027] Interference components (frequency) ):become High-frequency communication items.

[0028] Step 3: Intelligent bandwidth determination, which is the key to solving over-decomposition (AM signal splitting).

[0029] For baseband signals Perform spectrum analysis Examine the energy distribution near 0 Hz: Define the sideband energy ratio R: 1) If (Threshold): Determined to be an amplitude modulation / frequency modulation (AM / FM) signal. This indicates the presence of accompanying sidebands near the baseband.

[0030] Strategy: (Expand bandwidth to accommodate sidebands).

[0031] 2) If It is determined to be an independent single-frequency signal.

[0032] Strategy: (Extremely narrow bandwidth, neighboring nodes removed).

[0033] Step 4: Low-pass filtering extraction, applying a Gaussian low-pass filter to the baseband. Extract the complex envelope of the target mode: in .

[0034] Extracted baseband modes: Step 5: Remodulation recovery, shifting the extracted baseband envelope back to the original frequency. : Finally, the amplitude is corrected using orthogonal projection: Detailed explanation of each parameter in the formula: Example 1: To illustrate how this invention can suppress modal confusion, it will process unstable signals. First, consider the mixed signal shown in the following equation. x ( t ): (1) In the formula: , , The random noise has a mean of zero and follows a normal distribution. The time-domain waveforms of the mixed signal and its components are as follows: Figure 2 As shown.

[0035] The present invention is used to decompose the mixed signal, and the decomposition result is as follows: Figure 3 As shown in the figure, the decomposition yields three components. It can be seen from the figure that this invention effectively suppresses the mode confusion problem during decomposition and extracts components that are closer to the actual values. Components 2 and 1 obtained from the decomposition correspond to the actual components. and Component 3 is a noise signal, and its decomposition is ideal. The above simulation signal analysis results show that the present invention can accurately obtain the constituent components of complex information and has a good suppressive effect on mode confusion caused by noise interference.

[0036] Example 2: Consider another example of mode confusion caused by intermittent signals, a mixed signal consisting of a superposition of high-frequency intermittent signals and sinusoidal signals: (2) In the formula: , It consists of two intermittent signals. The mixed signal consists of a high-frequency intermittent signal and a 15Hz cosine signal, with the time-domain waveform as shown below. Figure 4 As shown.

[0037] The present invention is used to decompose the mixed signal, and the decomposition result is as follows: Figure 5 As shown, the decomposition yields two components. From Figure 4 It can be seen that the present invention effectively suppresses the mode confusion problem in the decomposition, and the component 1 obtained by decomposition corresponds to the actual component. Component 2 is the remaining term, and the decomposition result is ideal.

[0038] Example 3: To verify the feasibility of this method, mixed signals were examined. x ( t ): (3) In the formula: , , It is a white noise sequence with a mean of 0. .

[0039] Signal x ( t ) consisting of an amplitude-modulated and frequency-modulated signal x 1( t ) and a cosine signal x 2( t The time-domain waveform is formed by superposition of these elements. Figure 6 As shown. Using the present invention to... x ( t The decomposition is performed, and the decomposition result is as follows: Figure 7 As shown in the figure, the decomposition yields three components, with component 1 corresponding to the cosine signal. x 2( t ), component 2 corresponds to amplitude modulation and frequency modulation signals. x 1( t The two components obtained are very realistic, and the decomposition effect is excellent. Component 3 is the remaining term. Therefore, it can be seen that this invention is based on the decomposition of the signal itself, and each component obtained has a certain physical meaning, reflecting the intrinsic nature of the signal.

[0040] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM).

[0041] It should be understood that the above detailed description of the technical solutions of the present invention with reference to preferred embodiments is illustrative and not restrictive. Those skilled in the art can modify the technical solutions described in the embodiments or substitute some of the technical features based on reading this specification; however, these modifications or substitutions do not cause the essence of the corresponding technical solutions to depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for decomposing non-stationary signals based on adaptive frequency scanning demodulation, characterized in that: The method includes the following steps: Precise frequency locking: For noisy signals, the seed frequency is first roughly estimated through frequency domain analysis. Within the preset frequency range, for each candidate frequency, an optimization algorithm is used to search for the precise center frequency that maximizes the low-frequency energy of the signal after complex exponential demodulation. Synchronous demodulation: Based on the obtained precise center frequency, an orthogonal carrier is constructed to downconvert the noisy signal to the baseband, so that the target component becomes a DC component and the interference component is converted into a high-frequency AC term; Intelligent bandwidth determination: Perform spectrum analysis on the baseband signal, extract the energy distribution of DC and its adjacent range, and determine whether it is an amplitude modulation or frequency modulation signal based on the sideband energy ratio. Expand the bandwidth to include the sideband. If it is determined to be an independent single-frequency signal, use an extremely narrow bandwidth method to isolate the target component. Low-pass filter extraction: A Gaussian low-pass filter is applied to the baseband to extract the complex envelope of the target mode. The filter bandwidth is dynamically set according to the intelligent bandwidth determination step. Remodulation recovery: The extracted baseband envelope data is moved back to the original frequency, and the amplitude is corrected by orthogonal projection to finally obtain the target mode signal.

2. The non-stationary signal decomposition method based on adaptive frequency scanning demodulation according to claim 1, characterized in that: The precise frequency locking specifically includes: Noisy signal is provided Extracting the narrowband components with unknown frequencies ; First, a seed frequency is roughly estimated using FFT. Construct an optimization problem to find a frequency. This maximizes the low-frequency (DC) energy of the signal after complex exponential demodulation. ; When the demodulation frequency f is exactly equal to the signal frequency f k Only when a constant term (DC component) appears in the product term will the integral value be maximized; The fminbnd optimization algorithm is used to search over a continuous domain.

3. The non-stationary signal decomposition method based on adaptive frequency scanning demodulation according to claim 1, characterized in that: The intelligent bandwidth determination identifies the sideband energy ratio based on the energy distribution of the baseband spectrum and dynamically adjusts the filter bandwidth according to the evaluation results; For baseband signals Perform spectrum analysis Check the energy distribution near 0 Hz: Define the sideband energy ratio R: ; 1) If , Threshold: Determined to be an amplitude modulation / frequency modulation (AM / FM) signal; This indicates the presence of associated sidebands near the baseband; Strategy: Expand bandwidth and accommodate sidebands; 2) If It is determined to be an independent single-frequency signal; Strategy: Extremely narrow bandwidth, cut off neighbors.

4. The non-stationary signal decomposition method based on adaptive frequency scanning demodulation according to claim 1, characterized in that: The aforementioned synchronous demodulation specifically includes: Precise frequency obtained by locking Construct orthogonal carrier signals and downconvert the target component to baseband: ; Expand signal components: Target component (frequency) ): becomes 0Hz; Interference components (frequency) ):become High-frequency communication items.

5. The non-stationary signal decomposition method based on adaptive frequency scanning demodulation according to claim 1, characterized in that: The low-pass filter extraction uses a Gaussian low-pass filter to filter the baseband signal, and the filter bandwidth corresponds to the output of the bandwidth determination step. Application of Gaussian low-pass filters in baseband Extract the complex envelope of the target mode: ,in ; Extracted baseband modes: .

6. The non-stationary signal decomposition method based on adaptive frequency scanning demodulation according to claim 1, characterized in that: The remodulation recovery uses an orthogonal projection method to correct the amplitude of the target component, thus resisting error signals introduced during demodulation. The extracted baseband envelope is moved back to the original frequency. : ; Finally, the amplitude is corrected using orthogonal projection: 。 7. The non-stationary signal decomposition method based on adaptive frequency scanning demodulation according to claim 1, characterized in that: The method can recursively iterate over multi-component non-stationary signals to extract multiple different frequency components from the signal.

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