[CM] SND docs example: FM synthesis vs. additive synthesis

[Markus B]

Hi,

currently try to familiarize myself with the theories behind FM synthesis.
I found this page with a lot of useful information about FM synthesis:
https://ccrma.stanford.edu/software/snd/snd/fm.html

One can find an example on the linked page where the author compares FM
to additive synthesis. He states that the FM synthesis sounds louder and
richer. He also provided an image of both signals. I'm interested to
recreate this example on my own. I would like to use an example like that
for a term paper in my university.

The example is in the upper third of the page. Right after the 3D Bessel
plot and the three frequency spectrums but before the sum of multiple sinus
waves. The author wrote:


*'One hidden aspect of the FM expansion is that it produces a time domain
waveform that is not "spikey". If we add cosines at the amplitudes given by
the Bessel functions (using additive synthesis to produce the same
magnitude spectrum as FM produces), we get a very different waveform.
Doesn't the FM version sound richer and, far more importantly, louder?'*

I'm aware that the additive synthesis is basically a Fourier Series which
sums the different sideband frequencies up. I'm also aware how to create a
frequency spectrum for the FM synthesis, following Chownings paper or
Wikipedias formula. [1]

So how can I reproduce the shown signals from the page? The FM synthesis
seems to have a quite high carrier frequency, a relative low modulation
frequency and a modulation index of 3. But after I calculate the amplitudes
of the sideband frequencies and but them together to a additive synthesis,
I basically recreate the original FM synthesis. Which makes sense because I
just used the sum form of the FM synthesis formula.

That's why I'm confused how the author of the webpage could create the
aforementioned example?


Thank you for any help!

Markus

[1]
http://en.wikipedia.org/wiki/Frequency_modulation_synthesis#Spectral_analysis
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