function x=ifmt(mellin,beta,M);%IFMT	Inverse fast Mellin transform.%	X=IFMT(MELLIN,BETA,M) computes the inverse fast Mellin%	transform of MELLIN.%	WARNING : the inverse of the Mellin transform is correct only %	if the Mellin transform has been computed from FMIN to 0.5 Hz, %	and if the original signal is analytic.%	%	MELLIN : Mellin transform to be inverted. Mellin must have been%	 obtained from FMT with frequency running from FMIN to 0.5 Hz.%	BETA : Mellin variable issued from FMT.%	M : number of points of the inverse Mellin transform. %					(default : length(MELLIN)).%	X : inverse Mellin transform with M points in time.%%	Example :   %	 sig=atoms(128,[64,0.25,32,1]); %	 [MELLIN,BETA]=fmt(sig,0.05,0.5,256); clf;%	 X=ifmt(MELLIN,BETA,128); plot(real(X)); hold; %	 plot(real(sig),'g'); hold; %%	See also : fmt, fft, ifft.%%	P. Goncalves 9-95 - O. Lemoine, June 1996. %	Copyright (c) 1995 Rice University - 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 N=length(mellin);if nargin<2, error('At least 2 input parameters required');elseif nargin==2, M=N;endNo2 = (N+rem(N,2))/2;q   = exp(1/(N*(beta(2)-beta(1))));fmin = 0.5/(q^(No2-1));% Inverse Mellin transform computation p = 0:(N-1);L = log(fmin)/log(q);S = fft(fftshift(mellin.*exp(-j*2*pi*L*(p/N-1/2))/(N*log(q))));S = S(1:No2);% Inverse Fourier transformk = (1:No2);x = zeros(M,1); t = (1:M)-(M+rem(M,2))/2-1;geo_f = fmin*(exp((k-1).*log(q))) ;itfmatx = zeros(M,No2);itfmatx = exp(2*i*t'*geo_f*pi);for k=1:M, x(k) = real(integ(itfmatx(k,:).*S,geo_f));end;x = hilbert(x);% NormalizationSP = fft(x); fmax=0.5;indmin = 1+round(fmin*(M-2));indmax = 1+round(fmax*(M-2));SPana = SP(indmin:indmax);nu = (indmin:indmax)'/M; SPp = SPana./nu;Esm = SPp'*SPana;x = x*norm(mellin)/sqrt(Esm);