function [ti,fi]=midpoint(t1,f1,t2,f2,k)%MIDPOINT Mid-point construction used in the interference diagram. %	[TI,FI]=MIDPOINT(T1,F1,T2,F2,K) gives the coordinates in the%	time-frequency plane of the interference-term corresponding to%	the points (T1,F1) and (T2,F2), for a distribution in the%	affine class perfectly localized on power-law group-delays of %	the form : tx(nu)=t0+c nu^(K-1).%%	T1 : time-coordinate of the first point%	F1 : frequency-coordinate of the first point (>0)%	T2 : time-coordinate of the second point%	F2 : frequency-coordinate of the second point (>0)%	K  : power of the group-delay law%	  K = 2    : Wigner-Ville %	  K = 1/2  : D-Flandrin%	  K = 0    : Bertrand (unitary) %	  K = -1   : Unterberger (active)%	  K = inf  : Margenau-Hill-Rihaczek%	TI : time-coordinate of the interference term%	FI : frequency-coordinate of the interference term%%	See also PLOTSID.%	P. Flandrin, September 1995 - F. Auger, April 1996.%	Copyright (c) 1996 by CNRS (France).%%	------------------- CONFIDENTIAL PROGRAM -------------------- %	This program can not be used without the authorization of its%	author(s). For any comment or bug report, please send e-mail to %	f.auger@ieee.org if f1<=0 | f2<=0, error('F1 and F2 must be >0');end[rt1,ct1]=size(t1);[rt2,ct2]=size(t2);[rf1,cf1]=size(f1);[rf2,cf2]=size(f2);if (rt1~=rt2|rt1~=rf1|rt1~=rf2) | (ct1~=ct2|ct1~=cf1|ct1~=cf2),  error('T1, T2, F1 and F2 must have the same size');endif rt1>ct1, error('T1 must be a row-vector');elseif rt2>ct2, error('T2 must be a row-vector');elseif rf2>cf2, error('F2 must be a row-vector');elseif rf1>cf1, error('F1 must be a row-vector');end if (k==2), fi=(f1+f2)/2; ti=(t1+t2)/2;elseif (k==inf), ti=[t1;t2]; fi=[f2;f1];else I=find(abs(f1-f2)>sqrt(eps)); if length(I)~=0,   if (k==1),   fi(I)=exp( (f1(I).*(log(f1(I))-1)-f2(I).*(log(f2(I))-1)) ./ ... 	(f1(I)-f2(I)));    ti(I)=(t1(I).*f1(I)-t2(I).*f2(I)) ./ (f1(I)-f2(I)) - ... 	(t1(I)-t2(I)) ./ (log(f1(I))-log(f2(I)));  elseif (k==0),   fi(I)=(f1(I)-f2(I))./(log(f1(I))-log(f2(I)));   ti(I)=(t1(I).*f1(I)-t2(I).*f2(I)) ./ (f1(I)-f2(I)) + ...         f1(I) .* f2(I) .* (t2(I)-t1(I)) .* ...    	(log(f1(I))-log(f2(I))) ./ (f2(I)-f1(I)).^2;   else   t0(I)=(t1(I).*f2(I).^(k-1)-t2(I).*f1(I).^(k-1)) ./ ... 	(f2(I).^(k-1)-f1(I).^(k-1));   fi(I)=((f1(I).^k-f2(I).^k) ./ (f1(I)-f2(I))/k).^(1/(k-1));   ti(I)=t0(I)+(t2(I)-t1(I)) ./ (f2(I).^(k-1)-f1(I).^(k-1)) .*fi(I).^(k-1);  end endend