% Y: Inputted data;
% Nstd: ratio of the standard deviation of the added noise and that of Y;
% NE: Ensemble member being used
% TNM: total number of modes (not including the trend)
%
function allmode=ceemd(Y,Nstd,NE,TNM)
% find data length
xsize=length(Y);
dd=1:1:xsize;
% Nornaliz data
Ystd=std(Y);
Y=Y/Ystd;
% Initialize saved data
TNM2=TNM+2;
for kk=1:1:TNM2,
for ii=1:1:xsize,
allmode(ii,kk)=0.0;
end
end
for iii=1:1:NE
% adding noise
for i=1:xsize,
temp=randn(1,1)*Nstd;
X1(i)=Y(i)+temp;
X2(i)=Y(i)-temp;
end
% sifting X1
xorigin = X1;
xend = xorigin;
% save the initial data into the first column
for jj=1:1:xsize
mode(jj,1) = xorigin(jj);
end
nmode = 1;
while nmode <= TNM,
xstart = xend;
iter = 1;
while iter<=5,
[spmax, spmin, flag]=extrema(xstart);
upper= spline(spmax(:,1),spmax(:,2),dd);
lower= spline(spmin(:,1),spmin(:,2),dd);
mean_ul = (upper + lower)/2;
xstart = xstart - mean_ul;
iter = iter +1;
end
xend = xend - xstart;
nmode=nmode+1;
% save a mode
for jj=1:1:xsize,
mode(jj,nmode) = xstart(jj);
end
end
% save the trend
for jj=1:1:xsize,
mode(jj,nmode+1)=xend(jj);
end
% add mode to the sum of modes from earlier ensemble members
allmode=allmode+mode;
%%%=============================================================
% sifting X2
xorigin = X2;
xend = xorigin;
% save the initial data into the first column
for jj=1:1:xsize,
mode(jj,1) = xorigin(jj);
end
nmode = 1;
while nmode <= TNM,
xstart = xend;
iter = 1;
while iter<=5,
[spmax, spmin, flag]=extrema(xstart);
upper= spline(spmax(:,1),spmax(:,2),dd);
lower= spline(spmin(:,1),spmin(:,2),dd);
mean_ul = (upper + lower)/2;
xstart = xstart - mean_ul;
iter = iter +1;
end
xend = xend - xstart;
nmode=nmode+1;
% save a mode
for jj=1:1:xsize,
mode(jj,nmode) = xstart(jj);
end
end
% save the trend
for jj=1:1:xsize,
mode(jj,nmode+1)=xend(jj);
end
% add mode to the sum of modes from earlier ensemble members
allmode=allmode+mode;
%fprintf('-');
end
% ensemble average
allmode=allmode/NE/2;
% Rescale mode to origional unit.
allmode=allmode*Ystd;
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