%BOUNDARY_CONDITIONS_EMD  extends an extrema set to limit edge effects on the interpolations%% % [TMIN,TMAX,ZMIN,ZMAX] = BOUNDARY_CONDITIONS_EMD(INDMIN,INDMAX,T,X,Z,NBSYM)%% inputs:%   - INDMIN, INDMAX: indices of minima and maxima in the real signal X%   - T: sampling times%   - X: real signal in which INDMIN and INDMAX are the indices of extrema%   - Z: signal which values are interpolated in the final envelope%   - NBSYM: number of points added to each end%% outputs:%   - TMIN, TMAX: extended sampling times%   - ZMIN, ZMAX: extended "extrema" set%% use:%   - for a real signal X:%     [TMIN,TMAX,ZMIN,ZMAX] = BOUNDARY_CONDITIONS_EMD(INDMIN,INDMAX,T,X,X,NBSYM)%   - for a complex signal Z and a direction PHI:%     X = exp(-i*PHI)*Z;%     [TMIN,TMAX,ZMIN,ZMAX] = BOUNDARY_CONDITIONS_EMD(INDMIN,INDMAX,T,X,Z,NBSYM)%% rem: it has to be noted that this function was originally written for the % classical EMD and adapted to the bivariate case without a proper study of its% effects. The edge effects problem for the bivariate EMD has not been studied yet. %% See also%  extr%% G. Rilling, last modification 3.2007% gabriel.rilling@ens-lyon.frfunction [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