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!