%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
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