[Signal Denoising] Based on variational nonlinear linear frequency modulation mode decomposition VNCMD to achieve nonlinear noise denoising in multi-signal modes with matlab code

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Content introduction

Signal denoising is an important signal processing technology that plays a key role in many fields. Whether in communication systems, medical imaging, or audio processing, signal denoising can effectively improve signal quality and accuracy. In recent years, methods based on variational nonlinear chirp mode decomposition (VNCMD) have achieved remarkable results in nonlinear noise denoising in multi-signal modes. This article will introduce the VNCMD method and its application in signal denoising.

VNCMD is a signal decomposition technique based on variational methods, which can decompose signals into multiple modes. Different from the traditional linear frequency modulation mode decomposition method, VNCMD can process nonlinear FM signals and has good robustness to noise. This gives VNCMD an advantage when dealing with multi-signal patterns containing nonlinear noise.

The basic principle of VNCMD is to achieve signal decomposition by minimizing the difference between signals and modes. Specifically, VNCMD obtains the decomposed pattern by minimizing the second-order norm of the difference between the signal and the pattern. This decomposition based on variational methods can effectively extract the main modes in the signal and has less impact on noise.

In nonlinear noise denoising in multi-signal modes, the VNCMD method can decompose the signal into multiple modes, including the main mode of the signal and the mode of the noise. By analyzing and processing noise patterns, VNCMD can accurately remove nonlinear noise from signals. This makes VNCMD more effective in dealing with noise problems in complex signals.

The application of VNCMD method in signal denoising has been widely researched and practiced. For example, in speech signal denoising, VNCMD can effectively remove environmental noise and improve the clarity and intelligibility of speech signals. In medical imaging, VNCMD can accurately extract lesion signals and remove noise interference, thereby improving diagnostic accuracy. In audio processing, VNCMD can remove noise and distortion in audio signals and improve audio quality.

However, although the VNCMD method has good results in signal denoising, it still has some challenges and limitations. First, the VNCMD method has high computational complexity and requires a large amount of computing resources. Secondly, the VNCMD method is sensitive to the number of signal modes and noise characteristics, and requires reasonable parameter selection and adjustment. In addition, the VNCMD method may have certain limitations when processing non-stationary signals.

In summary, the VNCMD method based on variational nonlinear linear frequency modulation mode decomposition has a good effect in denoising nonlinear noise in multi-signal modes. It can effectively extract the main modes in the signal and remove the influence of nonlinear noise. However, the VNCMD method still requires further research and improvement to improve its computational efficiency and applicability. It is believed that with the continuous development of technology, the VNCMD method will play an increasingly important role in the field of signal processing.

Part of the code

%%%%%%%%%%%%%% signal with intersecting IFs %%%%%%%%%%%%%%%%</code><code>clc</code> <code>clear</code><code>close all</code><code>SampFreq = 2000;</code><code>t = 0:1/SampFreq:1;</code><code>Sig1 = (1 + 0.5*cos(2*pi*t)).*cos(2*pi*(0.2 + 532*t -474*t.^2 + 369*t.^3));</code><code>IF1 = 532 - 948*t + 1107*t.^2;</code><code>Sig2 = (1 + 0.5*cos(2*pi*t)).*cos(2*pi*(0.8 + 50*t + 525*t.^2 -300*t.^3));</code><code>IF2 = 50 + 1050*t - 900*t.^2;</code><code> Sig = Sig1 + Sig2;</code><code>figure</code><code>set(gcf,'Position',[20 100 320 250]); </code><code>set(gcf,'Color ','w'); </code><code>plot(t,Sig,'linewidth',1);</code><code>xlabel('Time / Sec','FontSize',12,'FontName ','Times New Roman');</code><code>ylabel('Amplitude','FontSize',12,'FontName','Times New Roman');</code><code>set(gca, 'xtick',[0 0.2 0.4 0.6 0.8 1]);</code><code>set(gca,'FontSize',12)</code><code>set(gca,'linewidth',1);</code><code>axis([0 1 -4 4])</code><code>%% STFT</code><code>Ratio = 0;</code><code>figure</code><code>[Spec,f] = STFT(Sig',SampFreq,512,256);</code><code>imagesc(t,f,abs(Spec)); </code><code>axis([0 1 0 700]);</code><code>set(gcf,'Position',[20 100 320 250]); </code><code>xlabel('Time / Sec','FontSize',12,'FontName ','Times New Roman');</code><code>ylabel('Frequency / Hz','FontSize',12,'FontName','Times New Roman');</code><code>set( gca,'xtick',[0 0.2 0.4 0.6 0.8 1]);</code><code>set(gca,'YDir','normal')</code><code>set(gca,'FontSize', 12);</code><code>set(gcf,'Color','w'); </code><code>%% parameter setting</code><code>iniIF = [700*ones(1, length(t));20*ones(1,length(t))];% initial guess for the IFs for the three signal modes</code><code>alpha = 5e-6; </code><code> beta = 1e-6; % this parameter can be smaller which will be helpful for the convergence, but it may not properly track fast varying IFs</code><code>var = 0; % noise variance</code><code> tol = 1e-8;%</code><code>tic</code><code>[IFmset IA smset] = VNCMD(Sig,SampFreq,iniIF,alpha,beta,var,tol);</code><code>toc</code><code>?</code><code>%% Relative errors of the finally estimated IFs</code><code> RE1 = norm(IFmset(1,:,end)-IF1)/ norm(IF1)</code><code> RE2 = norm(IFmset(2,:,end)-IF2)/norm(IF2)</code><code>%% estimated IF</code><code>figure </code><code>plot(t,[IF1;IF2],'b','linewidth',3) % true IFs</code><code>hold on</code><code>plot(t, IFmset(:,:,end),'r','linewidth',3) % finally estimated IFs</code><code>set(gcf,'Position',[20 100 640 500]); </code> <code>xlabel('Time / Sec','FontSize',24,'FontName','Times New Roman');</code><code>ylabel('Frequency / Hz','FontSize',24,' FontName','Times New Roman');</code><code>set(gca,'xtick',[0 0.2 0.4 0.6 0.8 1]);</code><code>set(gca,'YDir', 'normal')</code><code>set(gca,'FontSize',24);</code><code>set(gca,'linewidth',2);</code><code>set(gcf ,'Color','w'); </code><code>axis([0 1 0 800])</code><code>%% Reconstructed modes</code><code>figure</code><code>set(gcf,'Position',[20 100 640 200]); </code><code>set(gcf,'Color','w'); </code><code>plot(t,smset (1,:,end),'linewidth',2) % estimated mode</code><code>hold on</code><code>plot(t,Sig1 - smset(1,:,end),'k ','linewidth',2) % estimation errors</code><code>hold on</code><code>plot(t,IA(1,:),'r','linewidth',3) % estimated IAs</code><code>xlabel('Time / Sec','FontSize',24,'FontName','Times New Roman');</code><code>ylabel('m1','FontSize', 24,'FontName','Times New Roman');set(gca,'YDir','normal')</code><code>set(gca,'FontSize',24);</code><code> set(gca,'linewidth',2); </code><code>axis([0 1 -1.9 1.9])</code><code>?</code><code>figure</code><code>set(gcf,'Position',[20 100 640 200]); </code><code>set(gcf,'Color','w'); </code><code>plot(t,smset( 2,:,end),'linewidth',2) % estimated mode</code><code>hold on</code><code>plot(t,Sig2 - smset(2,:,end),'k' ,'linewidth',2) % estimation errors</code><code>hold on</code><code>plot(t,IA(2,:),'r','linewidth',3) % estimated IAs </code><code>xlabel('Time/Sec','FontSize',24,'FontName','Times New Roman');</code><code>ylabel('m2','FontSize',24 ,'FontName','Times New Roman');set(gca,'YDir','normal')</code><code>set(gca,'FontSize',24);</code><code>set (gca,'linewidth',2); </code><code>axis([0 1 -1.9 1.9])</code><code>?

Operation results

References

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1 Improvements and applications of various intelligent optimization algorithms

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Convolutional neural network (CNN), LSTM, support vector machine (SVM), least squares support vector machine (LSSVM), extreme learning machine (ELM), kernel extreme learning machine (KELM), BP, RBF, width Learning, DBN, RF, RBF, DELM, XGBOOST, TCN realize wind power prediction, photovoltaic prediction, battery life prediction, radiation source identification, traffic flow prediction, load prediction, stock price prediction, PM2.5 concentration prediction, battery health status prediction, water body Optical parameter inversion, NLOS signal identification, accurate subway parking prediction, transformer fault diagnosis

2. Image processing

Image recognition, image segmentation, image detection, image hiding, image registration, image splicing, image fusion, image enhancement, image compressed sensing

3 Path planning

Traveling salesman problem (TSP), vehicle routing problem (VRP, MVRP, CVRP, VRPTW, etc.), UAV three-dimensional path planning, UAV collaboration, UAV formation, robot path planning, raster map path planning , multimodal transportation problems, vehicle collaborative UAV path planning, antenna linear array distribution optimization, workshop layout optimization

4 UAV application

UAV path planning, UAV control, UAV formation, UAV collaboration, UAV task allocation, and online optimization of UAV safe communication trajectories

5 Wireless sensor positioning and layout

Sensor deployment optimization, communication protocol optimization, routing optimization, target positioning optimization, Dv-Hop positioning optimization, Leach protocol optimization, WSN coverage optimization, multicast optimization, RSSI positioning optimization

6 Signal processing

Signal recognition, signal encryption, signal denoising, signal enhancement, radar signal processing, signal watermark embedding and extraction, EMG signal, EEG signal, signal timing optimization