Hey hey,
I've got a simple one oscillator phase modulation feedback loop like this:
anote init 0
aph phasor 220 ; 220Hz
aph = frac(aph + anote*.25)
anote table3 aph, 1, 1, 0, 1 ; f1 is a sine wave

How can I compute the amount of aliasing or the relative strength of harmonic 
above the Nyquest frequency, dependent on the frequency of the fundamental?

The reason: of course I'd like to avoid audible aliasing with higher 
fundamental frequencies and thus adjust the feedback level. - I know that 
there are formulas, but the ones I have seen in papers were unreadable to me, 
as a blind person, because they were represented as images or in PDFs as 
untranslatable character sequences, loosing subscripts, superscripts and other 
mathematical symbols.

Any help would be very much appreciated.

Thanks and best wishes,

Jeanette

--------
* website: http://juliencoder.de - for summer is a state of sound
* SoundCloud: https://soundcloud.com/jeanette_c

If there's nothing missing in my life
Then why do these tears come at night <3
(Britney Spears)

Csound mailing list
Csound@listserv.heanet.ie
https://listserv.heanet.ie/cgi-bin/wa?A0=CSOUND
Send bugs reports to
        https://github.com/csound/csound/issues
Discussions of bugs and features can be posted here

Have you looked at this site:

https://www.st-andrews.ac.uk/~www_pa/Scots_Guide/RadCom/part12/page1.html

PM is a lot like FM and the spectrum can be calculated with Bessel 
functions of different orders.
Knowing the spectrum will give you the highest frequency, although this 
might be very high.
The section about narrowband FM might be what you need.

I do not know about the feedback component.

Richard


On 30/10/17 13:10, Jeanette C. wrote:
> Hey hey,
> I've got a simple one oscillator phase modulation feedback loop like 
> this:
> anote init 0
> aph phasor 220 ; 220Hz
> aph = frac(aph + anote*.25)
> anote table3 aph, 1, 1, 0, 1 ; f1 is a sine wave
>
> How can I compute the amount of aliasing or the relative strength of 
> harmonic above the Nyquest frequency, dependent on the frequency of 
> the fundamental?
>
> The reason: of course I'd like to avoid audible aliasing with higher 
> fundamental frequencies and thus adjust the feedback level. - I know 
> that there are formulas, but the ones I have seen in papers were 
> unreadable to me, as a blind person, because they were represented as 
> images or in PDFs as untranslatable character sequences, loosing 
> subscripts, superscripts and other mathematical symbols.
>
> Any help would be very much appreciated.
>
> Thanks and best wishes,
>
> Jeanette
>
> --------
> * website: http://juliencoder.de - for summer is a state of sound
> * SoundCloud: https://soundcloud.com/jeanette_c
>
> If there's nothing missing in my life
> Then why do these tears come at night <3
> (Britney Spears)
>
> Csound mailing list
> Csound@listserv.heanet.ie
> https://listserv.heanet.ie/cgi-bin/wa?A0=CSOUND
> Send bugs reports to
>        https://github.com/csound/csound/issues
> Discussions of bugs and features can be posted here

Csound mailing list
Csound@listserv.heanet.ie
https://listserv.heanet.ie/cgi-bin/wa?A0=CSOUND
Send bugs reports to
        https://github.com/csound/csound/issues
Discussions of bugs and features can be posted here

Oct 30 2017, Richard has written:

> Have you looked at this site:
>
> https://www.st-andrews.ac.uk/~www_pa/Scots_Guide/RadCom/part12/page1.html
Hi Richard,
now I have, but the formulas are again encoded in images, which is,
alas, completely useless for a blind person. The rest of the content
reads very well and clearly though.

Best wishes,

Jeanette
...

--------
* website: http://juliencoder.de - for summer is a state of sound
* SoundCloud: https://soundcloud.com/jeanette_c

She's so lucky,
she's a star
But she cry, cry, cries in her lonely heart... <3
(Britney Spears)

Csound mailing list
Csound@listserv.heanet.ie
https://listserv.heanet.ie/cgi-bin/wa?A0=CSOUND
Send bugs reports to
        https://github.com/csound/csound/issues
Discussions of bugs and features can be posted here