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do any of you know how to convert a FM index to a phase mod index equivalent considering they both have the same carrier and modulator frequency? Is it even possible?

This is in respect for sound synthesis and I'm talking about one sinusoid modulating another sinusoidal oscillator.

I'm being able to get very similar sounds with these parameters:

FM: carrier freq 200Hz, modulator freq 480Hz, index 400*

  • this means the carrier freq oscillates 400Hz up then back to original frequency and then down 400Hz and back 480 times a second

Phase Mod: carrier freq 200Hz, modulator freq 480Hz, index pi/4 **

** this index means the phase goes up 1/8 of a cycle and then back, down the same amount and back to the original point

FM and Phase Mod are clearly two independent processes, but I've seen people mention it can be equivalent, but I've never read anything that would tell me how to get the same results with both. So I don't know if it can really be done even if it sounds practically the same thing or if I just got lucky.

thanks

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phase is the integral (w.r.t. time) of frequency. and they are definitely not two independent processes. back in, i dunno, the 30s, Armstrong implemented FM for the first time using AM and a synchronized carrier that was 90° out of phase with the AM. so he was first accomplishing phase modulation (PM) out of AM (for which they had the existing technology - they didn't really have VCOs back in that day), then he implemented FM out of the PM by integrating the audio modulation signal and applying that to the PM modulation input.

this is all in a basic communications systems textbook like that of AB Carlson.

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  • $\begingroup$ so how can one convert the modulation index to get exact same sound synthesis for the same carrier and modulation frequency? I can't find anything about it. I got this similar results I mentioned in the original post by pure accident. thanks $\endgroup$
    – Alexandre Torres Porres
    Commented Aug 24, 2014 at 20:49
  • $\begingroup$ are you talking about FM synthesis of musical tones? like Chowning and the Yamaha DX7? $\endgroup$
    – robert bristow-johnson
    Commented Aug 26, 2014 at 14:54
  • $\begingroup$ yep, exactly. By the way, I was told DX7 uses PM and not FM. Cheers $\endgroup$
    – Alexandre Torres Porres
    Commented Aug 28, 2014 at 19:52
  • $\begingroup$ okay, so think of $$ \sin( \theta(t) ) = \sin\left( 2 \pi \int_0^t f(u) \ du + \theta(0) \right) $$ or $$ \sin\left( 2 \pi \int_0^t I \cdot x(u) \ du + \theta(0) \right) $$ where $x(t) \le 1$ is your modulating signal. and $I$ is the modulation index. $\endgroup$
    – robert bristow-johnson
    Commented Aug 28, 2014 at 20:48
  • $\begingroup$ I'm sorry but I'm not good at the math and needed a more straightforward formula convert the index from one case to the other considering same carrier & mod freqs - where the index in FM is in Hz, and is in radians in PM. What you wrote seems to be what this link also says moinsound.wordpress.com/2011/03/04/… or so I believe, but if it is it doesn't get me there yet. Thanks anyhow $\endgroup$
    – Alexandre Torres Porres
    Commented Sep 1, 2014 at 3:42

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