MATLAB中调用eemd函数
#MATLAB 中调用EEMD 函数
一般情况添加eemd.m和extrema.m到主函数的同一个文件夹就可直接调用了。
eemd.m中是英文注释，解释该函数各个参量的意义以及如何取值。
function allmode=eemd(Y,Nstd,NE)
Y为输入，待分解的信号；
Nstd是所加噪声的标准差；
NE是加入噪声的次数，取值为10-50即可；
若输入矩阵是kn；
则输出矩阵n(m+1),其中m=fix(log2(N))-1；
输出矩阵的第一列为原始信号，第2,3…m列是分解出的IMF（本征模态分量），m+1列就是残余分量。
eemd.m
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; Nstd = (0.1 ~ 0.4)*std(Y).
% NE: Ensemble number for the EEMD, NE = 10-50.
% 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 N*TNM2 matrix
TNM=fix(log2(xsize))-5; % TNM=m
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; % add a random noise to Y
X1(i)=Y(i)+temp;
end
%part4 --assign original data in the first column
for jj=1:1:xsize,
mode(jj,1) = Y(jj); % assign Y to column 1of mode
end
%part5--give initial 0to 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
%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
%part10--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 IMFs+overall trend ---those are all in mode
allmode=allmode+mode;
end %part3 Do EEMD -----EEMD loop end
%part11--devide EEMD summation by NE,std be multiply back to data
allmode=allmode/NE;
allmode=allmode*Ystd;
extrema.m
% This is a utility program for significance test.
%
% function [spmax, spmin, flag]= extrema(in_data)
%
% INPUT:
% in_data: Inputted data, a time series to be sifted（被筛选）;
% OUTPUT:
% spmax: The locations (col 1) of the maxima and its corresponding
% values (col 2)
% spmin: The locations (col 1) of the minima and its corresponding
% values (col 2)
%
% References can be found in the "Reference" section.
%
% The code is prepared by Zhaohua Wu. For questions, please read the "Q&A" section or
% contact
% [email protected]
%
function [spmax, spmin, flag]= extrema(in_data)
flag=1;
dsize=length(in_data);
spmax(1,1) = 1;
spmax(1,2) = in_data(1);
jj=2;
kk=2;
while jj=in_data(jj+1) )
spmax(kk,1) = jj;
spmax(kk,2) = in_data (jj);
kk = kk+1;
end
jj=jj+1;
end
spmax(kk,1)=dsize;
spmax(kk,2)=in_data(dsize);
if kk>=4
slope1=(spmax(2,2)-spmax(3,2))/(spmax(2,1)-spmax(3,1));
tmp1=slope1*(spmax(1,1)-spmax(2,1))+spmax(2,2);
if tmp1>spmax(1,2)
spmax(1,2)=tmp1;
end
slope2=(spmax(kk-1,2)-spmax(kk-2,2))/(spmax(kk-1,1)-spmax(kk-2,1));
tmp2=slope2*(spmax(kk,1)-spmax(kk-1,1))+spmax(kk-1,2);
if tmp2>spmax(kk,2)
spmax(kk,2)=tmp2;
end
else
flag=-1;
end
msize=size(in_data);
dsize=max(msize);
xsize=dsize/3;
xsize2=2*xsize;
spmin(1,1) = 1;
spmin(1,2) = in_data(1);
jj=2;
kk=2;
while jj=in_data(jj) & in_data(jj)<=in_data(jj+1))
spmin(kk,1) = jj;
spmin(kk,2) = in_data (jj);
kk = kk+1;
end
jj=jj+1;
end
spmin(kk,1)=dsize;
spmin(kk,2)=in_data(dsize);
if kk>=4
slope1=(spmin(2,2)-spmin(3,2))/(spmin(2,1)-spmin(3,1));
tmp1=slope1*(spmin(1,1)-spmin(2,1))+spmin(2,2);
if tmp1