function [x,iflaw] = fmhyp(N,p1,p2)%FMHYP	Signal with hyperbolic frequency modulation.%	[X,IFLAW]=FMHYP(N,P1,P2) generates a signal with hyperbolic%	frequency modulation : X(t) = exp(i.2.pi(F0.t + C/log|t|)) %%	N  : number of points in time%	P1 : if the number of input arguments (NARGIN) is 2, P1 is a %	    vector containing the two coefficients [F0 C] for an%	    hyperbolic instantaneous frequency or [T0 C] for an%	    hyperbolic group delay (sampling frequency is set to 1).%	    If NARGIN=3, P1 (as P2) is a time-frequency point of the %	    form [Ti Fi]. Ti is in seconds and Fi is a normalized frequency%	    (between 0 and 0.5). The coefficients F0 and C are then deduced%	    such that the frequency modulation law fits the points P1 and P2.%	P2 : same as P1 is NARGIN=3         (optional)%	X  : time row vector containing the modulated signal samples %	IFLAW : instantaneous frequency law%%	Examples :   %	 [X,IFLAW]=fmhyp(128,[1 .5],[32 0.1]);%	 subplot(211); plot(real(X));%	 subplot(212); plot(IFLAW);%%	See also FMLIN, FMSIN, FMPAR, FMCONST, FMODANY, FMPOWER.%	P. Goncalves - October 1995, O. Lemoine - November 1995%	Copyright (c) 1995 Rice University%%	------------------- 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 (nargin <= 1),  error ( 'The number of parameters must be at least 3.' );elseif (N <= 0), error ('The signal length N must be strictly positive' );elseif (nargin == 2)  if length(p1) ~= 2    error('Bad number of coefficients for P1');  end  f0 = p1(1) ;  c  = p1(2) ;elseif (nargin == 3) ;  if (length(p1) ~= 2) |(length(p2) ~= 2),    error('Bad number of coefficients for P1 or P2');  end  if p1(1)>N | p1(1)<1,   error ('P1(1) must be between 1 and N');  elseif p2(1)>N | p2(1)<1,   error ('P2(1) must be between 1 and N');  elseif p1(2)<0,   error ('P1(2) must be > 0');  elseif p2(2)<0,   error ('P2(2) must be > 0');  end  c = (p2(2) - p1(2))/(1/p2(1) - 1/p1(1)) ;  f0 = p1(2) - c/p1(1) ;end  t = 1:N ;phi = 2*pi*(f0*t + c*log(abs(t))); iflaw = (f0 + c*abs(t).^(-1)).' ;aliasing = find(iflaw < 0 | iflaw > 0.5) ;if isempty(aliasing) == 0 disp(['!!! WARNING: signal is undersampled or has negative frequencies']) ;endx = exp(i*phi).';