eemd.zip_EEMD_eemd.m_希-黄变换

%function allmode=eemd(Y,Nstd,NE) % % This is an EMD/EEMD program % % INPUT: % Y: Inputted data;1-d data only % Nstd: ratio of the standard deviation of the added noise and that of Y; % NE: Ensemble number for the EEMD % OUTPUT: % A matrix of N*(m+1) matrix, where N is the length of the input % data Y, and m=fix(log2(N))-1. Column 1 is the original data, columns 2, 3, ... % m are the IMFs from high to low frequency, and comlumn (m+1) is the % residual (over all trend). % % NOTE: % It should be noted that when Nstd is set to zero and NE is set to 1, the % program degenerates to a EMD program.(for EMD Nstd=0,NE=1) % This code limited sift number=10 ,the stoppage criteria can't change. % % References: % Wu, Z., and N. E Huang (2008), % Ensemble Empirical Mode Decomposition: a noise-assisted data analysis method. % Advances in Adaptive Data Analysis. Vol.1, No.1. 1-41. % % code writer: Zhaohua Wu. % footnote:S.C.Su 2009/03/04 % % There are three loops in this code coupled together. % 1.read data, find out standard deviation ,devide all data by std % 2.evaluate TNM as total IMF number--eq1. % TNM2=TNM+2,original data and residual included in TNM2 % assign 0 to TNM2 matrix % 3.Do EEMD NE times-------------------------------------------------------------loop EEMD start % 4.add noise % 5.give initial values before sift % 6.start to find an IMF------------------------------------------------IMF loop start % 7.sift 10 times to get IMF--------------------------sift loop start and end % 8.after 10 times sift --we got IMF % 9.subtract IMF from data ,and let the residual to find next IMF by loop % 6.after having all the IMFs---------------------------------------------IMF loop end % 9.after TNM IMFs ,the residual xend is over all trend % 3.Sum up NE decomposition result-------------------------------------------------loop EEMD end % 10.Devide EEMD summation by NE,std be multiply back to data % % Association: no % this function ususally used for doing 1-D EEMD with fixed % stoppage criteria independently. % % Concerned function: extrema.m % above mentioned m file must be put together function allmode=eemd(Y,Nstd,NE) %part1.read data, find out standard deviation ,devide all data by std xsize=length(Y); dd=1:1:xsize; Ystd=std(Y); Y=Y/Ystd; %part2.evaluate TNM as total IMF number,ssign 0 to TNM2 matrix TNM=fix(log2(xsize))-1; TNM2=TNM+2; for kk=1:1:TNM2, for ii=1:1:xsize, allmode(ii,kk)=0.0; end end %part3 Do EEMD -----EEMD loop start for iii=1:1:NE, %EEMD loop -NE times EMD sum together %part4 --Add noise to original data,we have X1 for i=1:xsize, temp=randn(1,1)*Nstd; X1(i)=Y(i)+temp; end %part4 --assign original data in the first column for jj=1:1:xsize, mode(jj,1) = Y(jj); end %part5--give initial 0 to xorigin and xend xorigin = X1; xend = xorigin; %part6--start to find an IMF-----IMF loop start nmode = 1; while nmode <= TNM, xstart = xend; %last loop value assign to new iteration loop %xstart -loop start data iter = 1; %loop index initial value %part7--sift 10 times to get IMF---sift loop start while iter<=10, [spmax, spmin, flag]=extrema(xstart); %call function extrema %the usage of spline ,please see part11. upper= spline(spmax(:,1),spmax(:,2),dd); %upper spline bound of this sift lower= spline(spmin(:,1),spmin(:,2),dd); %lower spline bound of this sift mean_ul = (upper + lower)/2;%spline mean of upper and lower xstart = xstart - mean_ul;%extract spline mean from Xstart iter = iter +1; end %part7--sift 10 times to get IMF---sift loop end %part8--subtract IMF from data ,then let the residual xend to start to find next IMF xend = xend - xstart; nmode=nmode+1; %part9--after sift 10 times,that xstart is this time IMF for jj=1:1:xsize, mode(jj,nmode) = xstart(jj); end end %part6--start to find an IMF-----IMF loop end %part 10--after gotten all(TNM) IMFs ,the residual xend is over all trend % put them in the last column for jj=1:1:xsize, mode(jj,nmode+1)=xend(jj); end %after part 10 ,original +TNM-IMF+overall trend ---those are all in mode allmode=allmode+mode; end %part3 Do EEMD -----EEMD loop end %part10--devide EEMD summation by NE,std be multiply back to data allmode=allmode/NE; allmode=allmode*Ystd; %part11--the syntax of the matlab function spline %yy= spline(x,y,xx); this means %x and y are matrixs of n1 points ,use n1 set (x,y) to form the cubic spline %xx and yy are matrixs of n2 points,we want know the spline value yy(y-axis) in the xx (x-axis)position %after the spline is formed by n1 points ,find coordinate value on the spline for [xx,yy] --n2 position.