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function [sscaled,mellin,beta] = dilate(s,a,fmin,fmax,N) ;
// This Software is ( Copyright INRIA . 1998 1 )
//
// INRIA holds all the ownership rights on the Software.
// The scientific community is asked to use the SOFTWARE
// in order to test and evaluate it.
//
// INRIA freely grants the right to use modify the Software,
// integrate it in another Software.
// Any use or reproduction of this Software to obtain profit or
// for commercial ends being subject to obtaining the prior express
// authorization of INRIA.
//
// INRIA authorizes any reproduction of this Software.
//
// - in limits defined in clauses 9 and 10 of the Berne
// agreement for the protection of literary and artistic works
// respectively specify in their paragraphs 2 and 3 authorizing
// only the reproduction and quoting of works on the condition
// that :
//
// - "this reproduction does not adversely affect the normal
// exploitation of the work or cause any unjustified prejudice
// to the legitimate interests of the author".
//
// - that the quotations given by way of illustration and/or
// tuition conform to the proper uses and that it mentions
// the source and name of the author if this name features
// in the source",
//
// - under the condition that this file is included with
// any reproduction.
//
// Any commercial use made without obtaining the prior express
// agreement of INRIA would therefore constitute a fraudulent
// imitation.
//
// The Software beeing currently developed, INRIA is assuming no
// liability, and should not be responsible, in any manner or any
// case, for any direct or indirect dammages sustained by the user.
//
// Any user of the software shall notify at INRIA any comments
// concerning the use of the Sofware (e-mail : FracLab@inria.fr)
//
// This file is part of FracLab, a Fractal Analysis Software
[nargout,nargin] = argn(0) ;
M = length(s) ;
if mtlb_rem(M,2) == 0
disp('--- WARNING --- length of signal to be scaled must be a odd number')
disp(' S zero-padded to the nearest odd length') ;
s = [s(:);0] ;
M = M+1 ;
end
T = M-1;
if nargin == 2
s = mtlb_fftshift(s) ; STF = fft(s,-1) ; s = mtlb_fftshift(s);
sp = (abs(STF(1:M/2))).^2;
f = linspace(0,0.5,M/2+1) ; f = f(1:M/2);
again = 'n';
while (again=='n' | again=='N')
plot(f,sp) ;
fmin = input('lower frequency bound = ') ;
fmax = input('upper frequency bound = ') ;
B = fmax-fmin ; R = B/((fmin+fmax)/2) ;
Nmin = (B*T*(1+2/R)*log((1+R/2)/(1-R/2)));
disp(['Number of frequency samples [ N >= ',string(ceil(Nmin)),' ] ']);
again = input('OK ? y/n = ','s');
end;
N = input('Frequency samples = ') ;
end
[mellin,beta] = dmt(s,fmin,fmax,N) ;
for na = 1 : length(a)
phase = exp((-%i*2*%pi*beta+1/2)*log(a(na))) ;
mellin_a = phase.*mellin ;
nta = 2*round((a(na)*M-1)/2) + 1 ;
sscaled(1,na) = nta ;
sscaled(2:nta+1,na) = idmt(mellin_a,beta,nta) ;
end
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