EEMD介绍和使用

1.什么是HHT？HHT就是先将信号进行经验模态分解（EMD分解），然后将分解后的每个IMF分量进行Hilbert变换，得到信号的时频属性的一种时频分析方法。2.EMD分解的步骤。EMD分解的流程图如下：3.实例演示。给定频率分别为10Hz和35Hz的两个正弦信号相叠加的复合信号，采样频率fs=2048Hz的信号，表达式如下：y=5sin(2*pi*10t)+5*sin(2*pi*35t)(1)为了对比，先用fft对求上述信号的幅频和相频曲线。1.functionfftfenxi2.clear;clc;3.N=2048;4.%fft默认计算的信号是从0开始的5.t=linspace(1,2,N);deta=t(2)-t(1);1/deta6.x=5*sin(2*pi*10*t)+5*sin(2*pi*35*t);7.%N1=256;N2=512;w1=0.2*2*pi;w2=0.3*2*pi;w3=0.4*2*pi;8.%x=(t=-200&t=-200+N1*deta).*sin(w1*t)+(t-200+N1*deta&t=-200+N2*deta).*sin(w2*t)+(t-200+N2*deta&t=200).*sin(w3*t);9.y=x;10.m=0:N-1;11.f=1./(N*deta)*m;%可以查看课本就是这样定义横坐标频率范围的12.%下面计算的Y就是x(t)的傅里叶变换数值13.%Y=exp(i*4*pi*f).*fft(y)%将计算出来的频谱乘以exp(i*4*pi*f)得到频移后[-2,2]之间的频谱值14.Y=fft(y);15.z=sqrt(Y.*conj(Y));16.plot(f(1:100),z(1:100));17.title('幅频曲线')18.xiangwei=angle(Y);19.figure(2)20.plot(f,xiangwei)21.title('相频曲线')22.figure(3)23.plot(t,y,'r')24.%axis([-2,2,0,1.2])25.title('原始信号')复制代码（2）用Hilbert变换直接求该信号的瞬时频率1.clear;clc;clf;2.%假设待分析的函数是z=t^33.N=2048;4.%fft默认计算的信号是从0开始的5.t=linspace(1,2,N);deta=t(2)-t(1);fs=1/deta;6.x=5*sin(2*pi*10*t)+5*sin(2*pi*35*t);7.z=x;8.hx=hilbert(z);9.xr=real(hx);xi=imag(hx);10.%计算瞬时振幅11.sz=sqrt(xr.^2+xi.^2);12.%计算瞬时相位13.sx=angle(hx);14.%计算瞬时频率15.dt=diff(t);16.dx=diff(sx);17.sp=dx./dt;18.plot(t(1:N-1),sp)19.title('瞬时频率')20.复制代码小结：傅里叶变换不能得到瞬时频率，即不能得到某个时刻的频率值。Hilbert变换是求取瞬时频率的方法，但如果只用Hilbert变换求出来的瞬时频率也不准确。（出现负频，实际上负频没有意义！）（3）用HHT求取信号的时频谱与边际谱1.functionHHT2.clear;clc;clf;3.N=2048;4.%fft默认计算的信号是从0开始的5.t=linspace(1,2,N);deta=t(2)-t(1);fs=1/deta;6.x=5*sin(2*pi*10*t)+5*sin(2*pi*35*t);7.z=x;8.c=emd(z);9.10.%计算每个IMF分量及最后一个剩余分量residual与原始信号的相关性11.[m,n]=size(c);12.fori=1:m;13.a=corrcoef(c(i,:),z);14.xg(i)=a(1,2);15.end16.xg;17.18.fori=1:m-119.%--------------------------------------------------------------------20.%计算各IMF的方差贡献率21.%定义：方差为平方的均值减去均值的平方22.%均值的平方23.%imfp2=mean(c(i,:),2).^224.%平方的均值25.%imf2p=mean(c(i,:).^2,2)26.%各个IMF的方差27.mse(i)=mean(c(i,:).^2,2)-mean(c(i,:),2).^2;28.end;29.mmse=sum(mse);30.fori=1:m-131.mse(i)=mean(c(i,:).^2,2)-mean(c(i,:),2).^2;32.%方差百分比，也就是方差贡献率33.mseb(i)=mse(i)/mmse*100;34.%显示各个IMF的方差和贡献率35.end;36.%画出每个IMF分量及最后一个剩余分量residual的图形37.figure(1)38.fori=1:m-139.disp(['imf',int2str(i)]);disp([mse(i)mseb(i)]);40.end;41.subplot(m+1,1,1)42.plot(t,z)43.set(gca,'fontname','timesNewRoman')44.set(gca,'fontsize',14.0)45.ylabel(['signal','Amplitude'])46.47.fori=1:m-148.subplot(m+1,1,i+1);49.set(gcf,'color','w')50.plot(t,c(i,:),'k')51.set(gca,'fontname','timesNewRoman')52.set(gca,'fontsize',14.0)53.ylabel(['imf',int2str(i)])54.end55.subplot(m+1,1,m+1);56.set(gcf,'color','w')57.plot(t,c(m,:),'k')58.set(gca,'fontname','timesNewRoman')59.set(gca,'fontsize',14.0)60.ylabel(['r',int2str(m-1)])61.62.%画出每个IMF分量及剩余分量residual的幅频曲线63.figure(2)64.subplot(m+1,1,1)65.set(gcf,'color','w')66.[f,z]=fftfenxi(t,z);67.plot(f,z,'k')68.set(gca,'fontname','timesNewRoman')69.set(gca,'fontsize',14.0)70.ylabel(['initialsignal',int2str(m-1),'Amplitude'])71.72.fori=1:m-173.subplot(m+1,1,i+1);74.set(gcf,'color','w')75.[f,z]=fftfenxi(t,c(i,:));76.plot(f,z,'k')77.set(gca,'fontname','timesNewRoman')78.set(gca,'fontsize',14.0)79.ylabel(['imf',int2str(i),'Amplitude'])80.end81.subplot(m+1,1,m+1);82.set(gcf,'color','w')83.[f,z]=fftfenxi(t,c(m,:));84.plot(f,z,'k')85.set(gca,'fontname','timesNewRoman')86.set(gca,'fontsize',14.0)87.ylabel(['r',int2str(m-1),'Amplitude'])88.89.hx=hilbert(z);90.xr=real(hx);xi=imag(hx);91.%计算瞬时振幅92.sz=sqrt(xr.^2+xi.^2);93.%计算瞬时相位94.sx=angle(hx);95.%计算瞬时频率96.dt=diff(t);97.dx=diff(sx);98.sp=dx./dt;99.figure(6)100.plot(t(1:N-1),sp)101.title('瞬时频率')102.103.%计算HHT时频谱和边际谱104.[A,fa,tt]=hhspectrum(c);105.[E,tt1]=toimage(A,fa,tt,length(tt));106.figure(3)107.disp_hhs(E,tt1)%二维图显示HHT时频谱，E是求得的HHT谱108.pause109.figure(4)110.fori=1:size(c,1)111.faa=fa(i,:);112.[FA,TT1]=meshgrid(faa,tt1);%三维图显示HHT时频图113.surf(FA,TT1,E)114.title('HHT时频谱三维显示')115.holdon116.end117.holdoff118.E=flipud(E);119.fork=1:size(E,1)120.bjp(k)=sum(E(k,:))*1/fs;121.end122.f=(1:N-2)/N*(fs/2);123.figure(5)124.plot(f,bjp);125.xlabel('频率/Hz');126.ylabel('信号幅值');127.title('信号边际谱')%要求边际谱必须先对信号进行EMD分解128.129.function[A,f,tt]=hhspectrum(x,t,l,aff)130.131.error(nargchk(1,4,nargin));132.133.ifnargin2134.135.t=1:size(x,2);136.137.end138.139.ifnargin3140.141.l=1;142.143.end144.145.ifnargin4146.147.aff=0;148.149.end150.151.ifmin(size(x))==1152.ifsize(x,2)==1153.x=x';154.ifnargin2155.t=1:size(x,2);156.end157.end158.Nmodes=1;159.else160.Nmodes=size(x,1);161.end162.163.lt=length(t);164.165.tt=t((l+1):(lt-l));166.167.fori=1:Nmodes168.169.an(i,:)=hilbert(x(i,:)')';170.f(i,:)=instfreq(an(i,:)',tt,l)';171.A=abs(an(:,l+1:end-l));172.173.ifaff174.disprog(i,Nmodes,max(Nmodes,100))175.end176.177.end178.179.180.functiondisp_hhs(im,t,inf)181.182.%DISP_HHS(im,t,inf)183.%displaysinanewfigurethespectrumcontainedinmatrixim184.%(amplitudesinlog).185.%186.%inputs:-im:imagematrix(e.g.,outputoftoimage)187.%-t(optional):timeinstants(e.g.,outputoftoimage)188.%-inf(optional):-dynamicrangeindB(wrtmax)189.%default:inf=-20190.%191.%utilisation:disp_hhs(im);disp_hhs(im,t);dis