%2007新出来的包含复数的emd函数(端点视作极值点)
function [imf,ort,nbits] = emd3(varargin)
[x,t,sd,sd2,tol,MODE_COMPLEX,ndirs,display_sifting,sdt,sd2t,r,imf,k,nbit,NbIt,MAXITERATIONS,FIXE,FIXE_H,MAXMODES,INTERP,mask] = init(varargin{:});
if display_sifting
fig_h = figure;
end
% 主循环 : 至少要求存在3个极值点，如果采用mask信号，不进入主循环
while ~stop_EMD(r,MODE_COMPLEX,ndirs) && (k < MAXMODES+1 || MAXMODES == 0) && ~any(mask)
% 当前模式
m = r;
% 前一次迭代的模式
mp = m;
% 计算均值和停止条件
if FIXE % 如果设定了迭代次数
[stop_sift,moyenne] = stop_sifting_fixe(t,m,INTERP,MODE_COMPLEX,ndirs);
elseif FIXE_H % 如果设定了迭代次数，且保留停止条件|#zeros-#extrema|<=1
stop_count = 0;
[stop_sift,moyenne] = stop_sifting_fixe_h(t,m,INTERP,stop_count,FIXE_H,MODE_COMPLEX,ndirs);
else % 采用默认停止条件
[stop_sift,moyenne] = stop_sifting(m,t,sd,sd2,tol,INTERP,MODE_COMPLEX,ndirs);
end
% 当前模式幅度过小，机器精度就可能引起虚假极值点的出现
if (max(abs(m))) < (1e-10)*(max(abs(x))) % IMF的最大值小于信号最大值的1e-10
if ~stop_sift % 如果筛过程没有停止
warning('emd:warning','forced stop of EMD : too small amplitude')
else
disp('forced stop of EMD : too small amplitude')
end
break
end
% 筛循环
while ~stop_sift && nbit<MAXITERATIONS
if(~MODE_COMPLEX && nbit>MAXITERATIONS/5 && mod(nbit,floor(MAXITERATIONS/10))==0 && ~FIXE && nbit > 100)
disp(['mode ',int2str(k),', iteration ',int2str(nbit)])
if exist('s','var')%查找是否存在变量s(var是指查找变量)
disp(['stop parameter mean value : ',num2str(s)])
end
[im,iM] = extr(m);
disp([int2str(sum(m(im) > 0)),' minima > 0; ',int2str(sum(m(iM) < 0)),' maxima < 0.'])
end
% 筛过程
m = m - moyenne;
% 计算均值和停止条件
if FIXE
[stop_sift,moyenne] = stop_sifting_fixe(t,m,INTERP,MODE_COMPLEX,ndirs);
elseif FIXE_H
[stop_sift,moyenne,stop_count] = stop_sifting_fixe_h(t,m,INTERP,stop_count,FIXE_H,MODE_COMPLEX,ndirs);
else
[stop_sift,moyenne,s] = stop_sifting(m,t,sd,sd2,tol,INTERP,MODE_COMPLEX,ndirs);
end
% 演示过程
if display_sifting && ~MODE_COMPLEX
NBSYM = 2;
[indmin,indmax] = extr(mp);
[tmin,tmax,mmin,mmax] = boundary_conditions(indmin,indmax,t,mp,mp,NBSYM);
envminp = interp1(tmin,mmin,t,INTERP);
envmaxp = interp1(tmax,mmax,t,INTERP);
envmoyp = (envminp+envmaxp)/2;
if FIXE || FIXE_H
display_emd_fixe(t,m,mp,r,envminp,envmaxp,envmoyp,nbit,k,display_sifting)
else
sxp = 2*(abs(envmoyp))./(abs(envmaxp-envminp));
sp = mean(sxp);
display_emd(t,m,mp,r,envminp,envmaxp,envmoyp,s,sp,sxp,sdt,sd2t,nbit,k,display_sifting,stop_sift)
end
end
mp = m;
nbit = nbit+1; % 单轮迭代计数
NbIt = NbIt+1; % 总体迭代计数
if (nbit==(MAXITERATIONS-1) && ~FIXE && nbit > 100)
if exist('s','var')
warning('emd:warning',['forced stop of sifting : too many iterations... mode ',int2str(k),'. stop parameter mean value : ',num2str(s)])
else
warning('emd:warning',['forced stop of sifting : too many iterations... mode ',int2str(k),'.'])
end
end
end % 筛循环
imf(k,:) = m;
if display_sifting
disp(['mode ',int2str(k),' stored'])
end
nbits(k) = nbit; % 记录每个IMF的迭代次数
k = k+1; % IMF计数
r = r - m; % 从原信号中减去提取的IMF
nbit = 0; % 单轮迭代次数清0
end % 主循环
% 计入残余信号
if any(r) && ~any(mask)
imf(k,:) = r;
end
% 计数正交指数
ort = io(x,imf);
% 关闭图形
if display_sifting
close
end
end
%---------------------------------------------------------------------------------------------------
% 测试是否存在足够的极值点（3个）进行分解，极值点个数小于3个则返回1，这是整体停止条件
function stop = stop_EMD(r,MODE_COMPLEX,ndirs)
if MODE_COMPLEX % 复信号情况
for k = 1:ndirs
phi = (k-1)*pi/ndirs;
[indmin,indmax] = extr(real(exp(i*phi)*r));
ner(k) = length(indmin) + length(indmax);
end
stop = any(ner < 3);
else % 实信号情况
[indmin,indmax] = extr(r);
ner = length(indmin) + length(indmax);
stop = ner < 3;
end
end
%---------------------------------------------------------------------------------------------------
% 计数包络均值和模式幅度估计值，返回包络均值
function [envmoy,nem,nzm,amp] = mean_and_amplitude(m,t,INTERP,MODE_COMPLEX,ndirs)
NBSYM = 2; % 边界延拓点数
if MODE_COMPLEX % 复信号情况
switch MODE_COMPLEX
case 1
for k = 1:ndirs
phi = (k-1)*pi/ndirs;
y = real(exp(-i*phi)*m);
[indmin,indmax,indzer] = extr(y);
nem(k) = length(indmin)+length(indmax);
nzm(k) = length(indzer);
[tmin,tmax,zmin,zmax] = boundary_conditions1(indmin,indmax,t,m);
envmin(k,:) = interp1(tmin,zmin,t,INTERP);
envmax(k,:) = interp1(tmax,zmax,t,INTERP);
end
envmoy = mean((envmin+envmax)/2,1);
if nargout > 3
amp = mean(abs(envmax-envmin),1)/2;
end
case 2
for k = 1:ndirs
phi = (k-1)*pi/ndirs;
y = real(exp(-i*phi)*m);
[indmin,indmax,indzer] = extr(y);
nem(k) = length(indmin)+length(indmax);
nzm(k) = length(indzer);
[tmin,tmax,zmin,zmax] = boundary_conditions1(indmin,indmax,t,m);
envmin(k,:) = exp(i*phi)*interp1(tmin,zmin,t,INTERP);
envmax(k,:) = exp(i*phi)*interp1(tmax,zmax,t,INTERP);
end
envmoy = mean((envmin+envmax),1);
if nargout > 3
amp = mean(abs(envmax-envmin),1)/2;
end
end
else % 实信号情况
[indmin,indmax,indzer] = extr(m); % 计数最小值、最大值和过零点位置
nem = length(indmin)+length(indmax);
nzm = length(indzer);
[tmin,tmax,mmin,mmax] = boundary_conditions1(indmin,indmax,t,m); % 边界延拓
envmin = interp1(tmin,mmin,t,INTERP);
envmax = interp1(tmax,mmax,t,INTERP);
envmoy = (envmin+envmax)/2;
if nargout > 3
amp = mean(abs(envmax-envmin),1)/2; % 计算包络幅度
end
end
end
%-------------------------------------------------------------------------------
% 默认停止条件，这是单轮迭代停止条件
function [stop,envmoy,s] = stop_sifting(m,t,sd,sd2,tol,INTERP,MODE_COMPLEX,ndirs)
try
[envmoy,nem,nzm,amp] = mean_and_amplitude(m,t,INTERP,MODE_COMPLEX,ndirs);
sx = abs(envmoy)./amp;
s = mean(sx);
stop = ~((mean(sx > sd) > tol | any(sx > sd2)) & (all(nem > 2))); % 停止准则（增加了极值点个数大于2）
if ~MODE_COMPLEX
stop = stop && ~(abs(nzm-nem)>1); % 对于实信号，要求极值点和过零点的个数相差1
end
catch
stop = 1;
envmoy = zeros(1,length(m));
s = NaN;
end
end
%-------------------------------------------------------------------------------
% 针对FIX选项的停止条件
function [stop,moyenne]= stop_sifting_fixe(t,m,INTERP,MODE_COMPLEX,ndirs)
try
moyenne = mean_and_amplitude(m,t,INTERP,MODE_COMPLEX,ndirs); % 正常情况下不会导致停止
stop = 0;
catch
moyenne = zeros(1,length(m));
stop = 1;
end
end
%-------------------------------------------------------------------------------
% 针对FIX_H选项的停止条件
function [stop,moyenne,stop_count]= stop_sifting_fixe_h(t,m,INTERP,stop_count,FIXE_H,MODE_COMPLEX,ndirs)
try
[moyenne,nem,nzm] = mean_and_amplitude(m,t,INTERP,MODE_COMPLEX,ndirs);
if (all(abs(nzm-nem)>1))
stop = 0;
stop_count = 0;
else % 极值点与过零点个数相差1后，还要达到指定次数才停止
stop_count = stop_count+1;
stop = (stop_count == FIXE_H);
end
catch
moyenne = zeros(1,length(m));
stop = 1;
end
end
%-------------------------------------------------------------------------------
% 演示分解过程（默认准则）
function display_emd(t,m,mp,r,envmin,envmax,envmoy,s,sb,sx,sdt,sd2t,nbit,k,display_sifting,stop_sift)
subplot(4,1,1)
plot(t,mp);hold on;
plot(t,envmax,'--k');plot(t,envmin,'--k');plot(t,envmoy,'r');
title(['IMF ',int2str(k),';
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