emd分解后画出IMF的波形

%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)functionfftfenxiclear;clc;N=2048;%fft默认计算的信号是从0开始的t=linspace(1,2,N);deta=t(2)-t(1);fs=1/deta;x=5*sin(2*pi*10*t)+5*sin(2*pi*35*t);N1=256;N2=512;w1=0.2*2*pi;w2=0.3*2*pi;w3=0.4*2*pi;%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);y=x;m=0:N-1;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%%%%%%%%%%%%%%%%%%%%%%%%%画出傅里叶频谱图%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%下面计算的Y就是x(t)的傅里叶变换数值%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Y=fft(y);z=sqrt(Y.*conj(Y));plot(f(1:100),z(1:100));title('幅频曲线')xiangwei=angle(Y);figure(2)plot(f,xiangwei)title('相频曲线')figure(3)plot(t,y,'r')%axis([-2,2,0,1.2])title('原始信号')%%%%%%%%%%%%%%%%%%%%用Hilbert变换直接求该信号的瞬时频率%%%%%%%%%%%%%%%%%%%%%clear;clc;clf;%假设待分析的函数是z=t^3N=2048;%fft默认计算的信号是从0开始的t=linspace(1,2,N);deta=t(2)-t(1);fs=1/deta;x=5*sin(2*pi*10*t)+5*sin(2*pi*35*t);z=x;hx=hilbert(z);xr=real(hx);xi=imag(hx);%计算瞬时振幅sz=sqrt(xr.^2+xi.^2);%计算瞬时相位sx=angle(hx);%计算瞬时频率dt=diff(t);dx=diff(sx);sp=dx./dt;plot(t(1:N-1),sp)title('瞬时频率')%%%%%%%%%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！）%%%%%%%%%%%%%%%%%%%%%%%用HHT求取信号的时频谱与边际谱%%%%%%%%%%%%%%%%%functionHHTclear;clc;clf;N=2048;%fft默认计算的信号是从0开始的t=linspace(1,2,N);deta=t(2)-t(1);fs=1/deta;x=5*sin(2*pi*10*t)+5*sin(2*pi*35*t);z=x;c=emd(z);%%%%%%%%%%%%%%%%%%画出每个IMF分量及最后一个剩余分量residual的图形%%%%%%%%%%%%%%%%%%画出imf矩阵的第一列元素，即原始数据subplot(m+1,1,1)plot(t,z)set(gca,'fontname','timesNewRoman')set(gca,'fontsize',14.0)ylabel(['signal','Amplitude'])%画出全部的IMF分量的图形fori=1:m-1subplot(m+1,1,i+1);set(gcf,'color','w')plot(t,c(i,:),'k')set(gca,'fontname','timesNewRoman')set(gca,'fontsize',14.0)ylabel(['imf',int2str(i)])end%画出最后一个剩余分量residual的波形subplot(m+1,1,m+1);set(gcf,'color','w')plot(t,c(m,:),'k')set(gca,'fontname','timesNewRoman')set(gca,'fontsize',14.0)ylabel(['r',int2str(m-1)])%%%%%%%%%%%%%%%%%%%%%%%画出每个IMF分量及剩余分量residual的幅频曲线%%%%%%%%%%%%%%%%%%%%%%%画出第一列原始数据的辐频曲线figure;subplot(m+1,1,1)set(gcf,'color','w')[f,z]=fftfenxi(t,z);plot(f,z,'k')set(gca,'fontname','timesNewRoman')set(gca,'fontsize',14.0)ylabel(['initialsignal',int2str(m-1),'Amplitude'])%画出每个IMF分量的辐频曲线fori=1:m-1subplot(m+1,1,i+1);set(gcf,'color','w')[f,z]=fftfenxi(t,c(i,:));plot(f,z,'k')set(gca,'fontname','timesNewRoman')set(gca,'fontsize',14.0)ylabel(['imf',int2str(i),'Amplitude'])end%画出最后一个剩余分量residual的辐频曲线subplot(m+1,1,m+1);set(gcf,'color','w')[f,z]=fftfenxi(t,c(m,:));plot(f,z,'k')set(gca,'fontname','timesNewRoman')set(gca,'fontsize',14.0)ylabel(['r',int2str(m-1),'Amplitude'])%%%%%%%%%%%%%%%%%%%%%%%%%%%%%计算HHT时频谱和边际谱%%%%%%%%%%%%%%%%%%%%%%%%%%%%[A,fa,tt]=hhspectrum(c);[E,tt1]=toimage(A,fa,tt,length(tt));figure(3)disp_hhs(E,tt1)%二维图显示HHT时频谱，E是求得的HHT谱pauseE=flipud(E);fork=1:size(E,1)bjp(k)=sum(E(k,:))*1/fs;endf=(1:N-2)/N*(fs/2);figure(5)plot(f,bjp);xlabel('频率/Hz');ylabel('信号幅值');title('信号边际谱')%要求边际谱必须先对信号进行EMD分解function[A,f,tt]=hhspectrum(x,t,l,aff)error(nargchk(1,4,nargin));ifnargin2t=1:size(x,2);endifnargin3l=1;endifnargin4aff=0;endifmin(size(x))==1ifsize(x,2)==1x=x';=1:size(x,2);endendNmodes=1;elseNmodes=size(x,1);endlt=length(t);tt=t((l+1):(lt-l));fori=1:Nmodesan(i,:)=hilbert(x(i,:)')';f(i,:)=instfreq(an(i,:)',tt,l)';A=abs(an(:,l+1:end-l));ifaffdisprog(i,Nmodes,max(Nmodes,100))(im,t,inf)%DISP_HHS(im,t,inf)%displaysinanewfigurethespectrumcontainedinmatrixim%(amplitudesinlog).%inputs:-im:imagematrix(e.g.,outputoftoimage)%-t(optional):timeinstants(e.g.,outputoftoimage)%-inf(optional):-dynamicrangeindB(wrtmax)%default:inf=-20%utilisation:disp_hhs(im);disp_hhs(im,t);disp_hhs(im,inf)%disp_hhs(im,t,inf)figurecolormap(bone)colormap(1-colormap);ifnargin==1inf=-20;t=1:size(im,2);==2iflength(t)==1inf=t;t=1:size(im,2);elseinf=-20;endendifinf=0error('infdoitetre0')endM=max(max(im));im=log10(im/M+1e-300);inf=inf/10;imagesc(t,fliplr((1:size(im,1))/(2*size(im,1))),im,[inf,0]);(gca,'YDir','normal')xlabel(['time'])ylabel(['normalizedfrequency'])title('Hilbert-Huangspectrum')function[f,z]=fftfenxi(t,y)L=length(t);N=2^nextpow2(L);%fft默认计算的信号是从0开始的t=linspace(t(1),t(L),N);deta=t(2)-t(1);m=0:N-1;f=1./(N*deta)*m;%下面计算的Y就是x(t)的傅里叶变换数值%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Y=fft(y);z=sqrt(Y.*conj(Y));