[sdiy] FM spectrum question

[ASSI]

On Freitag, 5. Mai 2006 17:29, jbv wrote:
> Don't know if it's the right place to ask but this is a question
> I wanted to ask for a long time : is there a way (simple or not
> - but I guess there's plenty of maths involved... may be is there
> a piece of software than can compute that), a way to know which
> parameters to use in FM synthesis (freqs, waveshapes...) in order
> to obtain a specific spectrum, in which the freq & amp of each
> partial is known in advance...

You really want to model a defined spectrum with a minimum number of FM 
operators? This is almost certainly an NP-hard problem in the general 
case, but if you skip the "minimum" requirement it should be amenable 
to heuristic search methods or genetic optimization. The forward 
problem of computing the spectrum from a known FM operator is solved by 
the following Octave function following the method from the book "FM 
Theory & Applications" by Chowning and Bristow (remove the comments to 
modify the plotting commands to suit your needs).


function [freqs,scale] = simplefm( fc, fm, mi, n )
# usage: fm( fc, fm, mi, n)
  cm=fc/fm;
  if (nargin < 4)
    n=mi+4;
  endif
  freqs=[(1-n*cm):cm:(1+n*cm)];
  scale=[fliplr(besselj((1:n),mi).*(-1).^(1:n)),besselj((0:n),mi)];
  [s,idx]=sort(abs(freqs(1,:)));
  fs=[
      fc*abs(freqs(:,idx));
      (-2*(freqs(:,idx)<0).+1).*scale(:,idx);
      ];
  [nr,nc]=size(fs);
  i=2;
  j=1;
  while (i<=nc)
    if (fs(1,i)==fs(1,i-1))
      fs(2,i)+=fs(2,i-1);
      fs(:,j)=fs(:,i++);
    else
      fs(:,++j)=fs(:,i++);
    endif
  endwhile
  fs=fs(:,1:j)';
#  plot( fc*freqs, scale, "^" );
#  hold on
#  gplot "0"
#  hold on
#  gplot fs with impulses;
#  hold on
  fs=abs(fs);
  gplot fs with impulses;
  hold off

endfunction



Achim.
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