emd.asv

2007版EMD(经验模态分解)完整程序

plot(t,mp);hold on;
plot(t,envmax,'--k');plot(t,envmin,'--k');plot(t,envmoy,'r');
title(['IMF ',int2str(k),';   iteration ',int2str(nbit),' before sifting']);
set(gca,'XTick',[])
hold  off
subplot(3,1,2)
plot(t,m)
title(['IMF ',int2str(k),';   iteration ',int2str(nbit),' after sifting']);
set(gca,'XTick',[])
subplot(3,1,3);
plot(t,r-m)
title('residue');
if display_sifting == 2
  pause(0.01)
else
  pause
end
end

%---------------------------------------------------------------------------------------
% defines new extrema points to extend the interpolations at the edges of the
% signal (mainly mirror symmetry)
function [tmin,tmax,zmin,zmax] = boundary_conditions(indmin,indmax,t,x,z,nbsym)
	
	lx = length(x);
	
	if (length(indmin) + length(indmax) < 3)
		error('not enough extrema')
	end

    % boundary conditions for interpolations :

	if indmax(1) < indmin(1)
    	if x(1) > x(indmin(1))
			lmax = fliplr(indmax(2:min(end,nbsym+1)));
			lmin = fliplr(indmin(1:min(end,nbsym)));
			lsym = indmax(1);
		else
			lmax = fliplr(indmax(1:min(end,nbsym)));
			lmin = [fliplr(indmin(1:min(end,nbsym-1))),1];
			lsym = 1;
		end
	else

		if x(1) < x(indmax(1))
			lmax = fliplr(indmax(1:min(end,nbsym)));
			lmin = fliplr(indmin(2:min(end,nbsym+1)));
			lsym = indmin(1);
		else
			lmax = [fliplr(indmax(1:min(end,nbsym-1))),1];
			lmin = fliplr(indmin(1:min(end,nbsym)));
			lsym = 1;
		end
	end
    
	if indmax(end) < indmin(end)
		if x(end) < x(indmax(end))
			rmax = fliplr(indmax(max(end-nbsym+1,1):end));
			rmin = fliplr(indmin(max(end-nbsym,1):end-1));
			rsym = indmin(end);
		else
			rmax = [lx,fliplr(indmax(max(end-nbsym+2,1):end))];
			rmin = fliplr(indmin(max(end-nbsym+1,1):end));
			rsym = lx;
		end
	else
		if x(end) > x(indmin(end))
			rmax = fliplr(indmax(max(end-nbsym,1):end-1));
			rmin = fliplr(indmin(max(end-nbsym+1,1):end));
			rsym = indmax(end);
		else
			rmax = fliplr(indmax(max(end-nbsym+1,1):end));
			rmin = [lx,fliplr(indmin(max(end-nbsym+2,1):end))];
			rsym = lx;
		end
	end
    
	tlmin = 2*t(lsym)-t(lmin);
	tlmax = 2*t(lsym)-t(lmax);
	trmin = 2*t(rsym)-t(rmin);
	trmax = 2*t(rsym)-t(rmax);
    
	% in case symmetrized parts do not extend enough
	if tlmin(1) > t(1) || tlmax(1) > t(1)
		if lsym == indmax(1)
			lmax = fliplr(indmax(1:min(end,nbsym)));
		else
			lmin = fliplr(indmin(1:min(end,nbsym)));
		end
		if lsym == 1
			error('bug')
		end
		lsym = 1;
		tlmin = 2*t(lsym)-t(lmin);
		tlmax = 2*t(lsym)-t(lmax);
	end   
    
	if trmin(end) < t(lx) || trmax(end) < t(lx)
		if rsym == indmax(end)
			rmax = fliplr(indmax(max(end-nbsym+1,1):end));
		else
			rmin = fliplr(indmin(max(end-nbsym+1,1):end));
		end
	if rsym == lx
		error('bug')
	end
		rsym = lx;
		trmin = 2*t(rsym)-t(rmin);
		trmax = 2*t(rsym)-t(rmax);
	end 
          
	zlmax =z(lmax); 
	zlmin =z(lmin);
	zrmax =z(rmax); 
	zrmin =z(rmin);
     
	tmin = [tlmin t(indmin) trmin];
	tmax = [tlmax t(indmax) trmax];
	zmin = [zlmin z(indmin) zrmin];
	zmax = [zlmax z(indmax) zrmax];
end
    
%---------------------------------------------------------------------------------------------------
%extracts the indices of extrema
function [indmin, indmax, indzer] = extr(x,t)

if(nargin==1)
  t=1:length(x);
end

m = length(x);

if nargout > 2
  x1=x(1:m-1);
  x2=x(2:m);
  indzer = find(x1.*x2<0);

  if any(x == 0)
    iz = find( x==0 );
    indz = [];
    if any(diff(iz)==1)
      zer = x == 0;
      dz = diff([0 zer 0]);
      debz = find(dz == 1);
      finz = find(dz == -1)-1;
      indz = round((debz+finz)/2);
    else
      indz = iz;
    end
    indzer = sort([indzer indz]);
  end
end

d = diff(x);

n = length(d);
d1 = d(1:n-1);
d2 = d(2:n);
indmin = find(d1.*d2<0 & d1<0)+1;
indmax = find(d1.*d2<0 & d1>0)+1;


% when two or more successive points have the same value we consider only one extremum in the middle of the constant area
% (only works if the signal is uniformly sampled)

if any(d==0)

  imax = [];
  imin = [];

  bad = (d==0);
  dd = diff([0 bad 0]);
  debs = find(dd == 1);
  fins = find(dd == -1);
  if debs(1) == 1
    if length(debs) > 1
      debs = debs(2:end);
      fins = fins(2:end);
    else
      debs = [];
      fins = [];
    end
  end
  if length(debs) > 0
    if fins(end) == m
      if length(debs) > 1
        debs = debs(1:(end-1));
        fins = fins(1:(end-1));

      else
        debs = [];
        fins = [];
      end
    end
  end
  lc = length(debs);
  if lc > 0
    for k = 1:lc
      if d(debs(k)-1) > 0
        if d(fins(k)) < 0
          imax = [imax round((fins(k)+debs(k))/2)];
        end
      else
        if d(fins(k)) > 0
          imin = [imin round((fins(k)+debs(k))/2)];
        end
      end
    end
  end

  if length(imax) > 0
    indmax = sort([indmax imax]);
  end

  if length(imin) > 0
    indmin = sort([indmin imin]);
  end

end
end

%---------------------------------------------------------------------------------------------------

function ort = io(x,imf)
% ort = IO(x,imf) computes the index of orthogonality
%
% inputs : - x    : analyzed signal
%          - imf  : empirical mode decomposition

n = size(imf,1);

s = 0;

for i = 1:n
  for j =1:n
    if i~=j
      s = s + abs(sum(imf(i,:).*conj(imf(j,:)))/sum(x.^2));
    end
  end
end

ort = 0.5*s;
end
%---------------------------------------------------------------------------------------------------

function [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)

x = varargin{1};
if nargin == 2
  if isstruct(varargin{2})
    inopts = varargin{2};
  else
    error('when using 2 arguments the first one is the analyzed signal X and the second one is a struct object describing the options')
  end
elseif nargin > 2
  try
    inopts = struct(varargin{2:end});
  catch
    error('bad argument syntax')
  end
end

% default for stopping
defstop = [0.05,0.5,0.05];

opt_fields = {'t','stop','display','maxiterations','fix','maxmodes','interp','fix_h','mask','ndirs','complex_version'};

defopts.stop = defstop;
defopts.display = 0;
defopts.t = 1:max(size(x));
defopts.maxiterations = 2000;
defopts.fix = 0;
defopts.maxmodes = 0;
defopts.interp = 'spline';
defopts.fix_h = 0;
defopts.mask = 0;
defopts.ndirs = 4;
defopts.complex_version = 2;

opts = defopts;



if(nargin==1)
  inopts = defopts;
elseif nargin == 0
  error('not enough arguments')
end


names = fieldnames(inopts);
for nom = names'
  if ~any(strcmpi(char(nom), opt_fields))
    error(['bad option field name: ',char(nom)])
  end
  if ~isempty(eval(['inopts.',char(nom)])) % empty values are discarded
    eval(['opts.',lower(char(nom)),' = inopts.',char(nom),';'])
  end
end

t = opts.t;
stop = opts.stop;
display_sifting = opts.display;
MAXITERATIONS = opts.maxiterations;
FIXE = opts.fix;
MAXMODES = opts.maxmodes;
INTERP = opts.interp;
FIXE_H = opts.fix_h;
mask = opts.mask;
ndirs = opts.ndirs;
complex_version = opts.complex_version;

if ~isvector(x)
  error('X must have only one row or one column')
end

if size(x,1) > 1
  x = x.';
end

if ~isvector(t)
  error('option field T must have only one row or one column')
end

if ~isreal(t)
  error('time instants T must be a real vector')
end

if size(t,1) > 1
  t = t';
end

if (length(t)~=length(x))
  error('X and option field T must have the same length')
end

if ~isvector(stop) || length(stop) > 3
  error('option field STOP must have only one row or one column of max three elements')
end

if ~all(isfinite(x))
  error('data elements must be finite')
end

if size(stop,1) > 1
  stop = stop';
end

L = length(stop);
if L < 3
  stop(3)=defstop(3);
end

if L < 2
  stop(2)=defstop(2);
end


if ~ischar(INTERP) || ~any(strcmpi(INTERP,{'linear','cubic','spline'}))
  error('INTERP field must be ''linear'', ''cubic'', ''pchip'' or ''spline''')
end

%special procedure when a masking signal is specified
if any(mask)
  if ~isvector(mask) || length(mask) ~= length(x)
    error('masking signal must have the same dimension as the analyzed signal X')
  end

  if size(mask,1) > 1
    mask = mask.';
  end
  opts.mask = 0;
  imf1 = emd(x+mask,opts);
  imf2 = emd(x-mask,opts);
  if size(imf1,1) ~= size(imf2,1)
    warning('emd:warning',['the two sets of IMFs have different sizes: ',int2str(size(imf1,1)),' and ',int2str(size(imf2,1)),' IMFs.'])
  end
  S1 = size(imf1,1);
  S2 = size(imf2,1);
  if S1 ~= S2
    if S1 < S2
      tmp = imf1;
      imf1 = imf2;
      imf2 = tmp;
    end
    imf2(max(S1,S2),1) = 0;
  end
  imf = (imf1+imf2)/2;

end


sd = stop(1);
sd2 = stop(2);
tol = stop(3);

lx = length(x);

sdt = sd*ones(1,lx);
sd2t = sd2*ones(1,lx);

if FIXE
  MAXITERATIONS = FIXE;
  if FIXE_H
    error('cannot use both ''FIX'' and ''FIX_H'' modes')
  end
end

MODE_COMPLEX = ~isreal(x)*complex_version;
if MODE_COMPLEX && complex_version ~= 1 && complex_version ~= 2
  error('COMPLEX_VERSION parameter must equal 1 or 2')
end


% number of extrema and zero-crossings in residual
ner = lx;
nzr = lx;

r = x;

if ~any(mask) % if a masking signal is specified "imf" already exists at this stage
  imf = [];
end
k = 1;

% iterations counter for extraction of 1 mode
nbit=0;

% total iterations counter
NbIt=0;
end
%---------------------------------------------------------------------------------------------------