function [x,iflaw]=fmpar(N,p1,p2,p3)%FMPAR	Parabolic frequency modulated signal.%	[X,IFLAW]=FMPAR(N,P1,P2,P3) generates a signal with%	parabolic frequency modulation law.%	X(T) = exp(j*2*pi(A0.T + A1/2.T^2 +A2/3.T^3)) %%	N  : the number of points in time%	P1 : if NARGIN=2, P1 is a vector containing the three %	    coefficients [A0 A1 A2] of the polynomial instantaneous phase.%	    If NARGIN=4, P1 (as P2 and P3) is a time-frequency point of %	    the form [Ti Fi].%	    The coefficients (A0,A1,A2) are then deduced such that  %	    the frequency modulation law fits these three points.%	P2,P3 : same as P1 if NARGIN=4.       (optional)%	X     : time row vector containing the modulated signal samples %	IFLAW : instantaneous frequency law%%	Examples :   %	 [X,IFLAW]=fmpar(128,[1 0.4],[64 0.05],[128 0.4]);%	 subplot(211);plot(real(X));subplot(212);plot(IFLAW);%	 [X,IFLAW]=fmpar(128,[0.4 -0.0112 8.6806e-05]);%	 subplot(211);plot(real(X));subplot(212);plot(IFLAW);%%	See also FMCONST, FMHYP, FMLIN, FMSIN, 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 2.' );elseif (N <= 0), error ('The signal length N must be strictly positive' );elseif nargin == 2 ;  if length(p1) ~= 3    error('Bad number of coefficients for P1');  end  a0 = p1(1) ; a1 = p1(2) ; a2 = p1(3) ;elseif nargin == 4 ;  if (length(p1) ~= 2) |(length(p2) ~= 2) |(length(p3) ~= 2),    error('Bad number of coefficients for P1, P2, P3');  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 p3(1)>N | p3(1)<1,   error ('P3(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');  elseif p3(2)<0,   error ('P3(2) must be > 0');  end  Y = [p1(2) p2(2) p3(2)] ;  X = [1 1 1;p1(1) p2(1) p3(1);p1(1)^2 p2(1)^2 p3(1)^2] ;  coef = Y*inv(X) ;   a0 = coef(1) ;  a1 = coef(2) ;  a2 = coef(3) ;end  t=1:N;phi = 2*pi*(a0*t + a1/2*t.^2 + a2/3*t.^3) ;iflaw = (a0 + a1*t + a2*t.^2).' ;aliasing = find(iflaw<0 | iflaw>0.5) ;if isempty(aliasing) == 0  disp(['!!! WARNING: signal is undersampled or has negative frequencies']) ;endx = exp(i*phi).';