Hi all,

this might be slightly off topic but I need help with some simple sound-related math. I've been trying to do something as trivial as plotting the function of a wave modulated by another one.

At the moment i'm using this function:

[1] **y = cos(Fc * x + M * cos(Fm * x))**

Function plot on Wolfram Alpha

Where *Fm* is the frequency of the modulator, *Fc* frequency of the carrier and *M* the modulation index. In this way I can draw two sine waves modulating each other and - surprisingly enough - this also works when modulating the frequency of other waveshapes, like a [x - floor(x)] sawtooth:

[2] **y = [Fc * x + M * cos(Fm * x)] - floor(Fc * x + M * cos(Fm * x))**

Function plot on Wolfram Alpha

BUT I can't manage to do the opposite! If I want a sinewave to be frequency modulated by a sawtooth wave it just doesn't work. I see the phase going all crazy but no frequency modulation at all.

[3] **y = cos(Fc * x + M * [(Fm * x) - floor(Fm * x)])**

Function plot on Wolfram Alpha

Am I taking a completely wrong approach? What elementary mathematical principle am I missing here? Thanks!