spectra of fm-sounds

Dear community,
I remember, there was a possibility to calculate the partials of a spectrum
generated with fm-modulation, but I couldn't find this feature.
Does somebody of You know how to do this?

On Mon, Jan 10, 2011 at 3:07 PM, Stefan Thomas
<kontrapunktstefan@...> wrote:
>
> Dear community,
> I remember, there was a possibility to calculate the partials of a spectrum generated with fm-modulation, but I couldn't find this feature.
> Does somebody of You know how to do this?

1) Set up a magnitude response graph, e.g. w vs |F(w)|, where w is frequency
2) Plot the carrier frequency c as an impulse on this graph at w=c
3) Let m be the modulating frequency. Plot impulses at w=c+m, c+2m,
c+3m, etc... and w=c-m, c-2m, c-3m, etc...
4) The amplitude of each impulse is related to the Bessel functions of
the nth kind: http://en.wikipedia.org/wiki/Bessel_function

I don't remember the exact formula for the amplitude, but you can
probably find it pretty easily by googling "fm bessel function." The
general idea, though is that an infinite series sidebands are
generated at spacing m around carrier c. Negative frequencies reflect
into the positive side of the spectrum, but with altered phase (I
think altered by 90 degrees, not sure).

-Mike