function [fnormhat,t]=instfreq(x,t,L,trace);%INSTFREQ Instantaneous frequency estimation.%	[FNORMHAT,T]=INSTFREQ(X,T,L,TRACE) computes the instantaneous %	frequency of the analytic signal X at time instant(s) T, using the%	trapezoidal integration rule.%	The result FNORMHAT lies between 0.0 and 0.5.% %	X : Analytic signal to be analyzed.%	T : Time instants	        (default : 2:length(X)-1).%	L : If L=1, computes the (normalized) instantaneous frequency %	    of the signal X defined as angle(X(T+1)*conj(X(T-1)) ;%	    if L>1, computes a Maximum Likelihood estimation of the%	    instantaneous frequency of the deterministic part of the signal%	    blurried in a white gaussian noise.%	    L must be an integer       	(default : 1).%	TRACE : if nonzero, the progression of the algorithm is shown%	                                (default : 0).%	FNORMHAT : Output (normalized) instantaneous frequency.%	T : Time instants.%%	Examples : %	 x=fmlin(70,0.05,0.35,25); [instf,t]=instfreq(x); plot(t,instf)%	 N=64; SNR=10.0; L=4; t=L+1:N-L; x=fmsin(N,0.05,0.35,40);%	 sig=sigmerge(x,hilbert(randn(N,1)),SNR);%	 plotifl(t,[instfreq(sig,t,L),instfreq(x,t)]); grid;%	 title ('theoretical and estimated instantaneous frequencies');%%	See also  KAYTTH, SGRPDLAY.%	F. Auger, March 1994, July 1995.%	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 (nargin == 0), error('At least one parameter required');end;[xrow,xcol] = size(x);if (xcol~=1), error('X must have only one column');endif (nargin == 1), t=2:xrow-1; L=1; trace=0.0;elseif (nargin == 2), L = 1; trace=0.0;elseif (nargin == 3), trace=0.0;end;if L<1, error('L must be >=1');end[trow,tcol] = size(t);if (trow~=1), error('T must have only one row'); end;if (L==1), if any(t==1)|any(t==xrow),  error('T can not be equal to 1 neither to the last element of X'); else  fnormhat=0.5*(angle(-x(t+1).*conj(x(t-1)))+pi)/(2*pi); end;else H=kaytth(L);  if any(t<=L)|any(t+L>xrow),  error('The relation L<T<=length(X)-L must be satisfied'); else  for icol=1:tcol,   if trace, disprog(icol,tcol,10); end;   ti = t(icol); tau = 0:L;   R = x(ti+tau).*conj(x(ti-tau));   M4 = R(2:L+1).*conj(R(1:L));      diff=2e-6;   tetapred = H * (unwrap(angle(-M4))+pi);   while tetapred<0.0 , tetapred=tetapred+(2*pi); end;   while tetapred>2*pi, tetapred=tetapred-(2*pi); end;   iter = 1;   while (diff > 1e-6)&(iter<50),    M4bis=M4 .* exp(-j*2.0*tetapred);    teta = H * (unwrap(angle(M4bis))+2.0*tetapred);    while teta<0.0 , teta=(2*pi)+teta; end;    while teta>2*pi, teta=teta-(2*pi); end;    diff=abs(teta-tetapred);    tetapred=teta; iter=iter+1;   end;   fnormhat(icol,1)=teta/(2*pi);  end; end;end;