I try to get my sound program right, and hoped to find some help here with the understanding of frequency modulation by a square wave.
My modulation looks like this: (please excuse if my formula naming and writing is not standard, glad to learn it)
$$y_m=A \cdot sin( 2 \pi f_c x + \\I \cdot \color{green}{( \frac4 \pi \frac 1 1 sin(1 \pi f_mx) + \frac 4 \pi \frac 1 3 sin(3 \pi f_mx) + \frac 4 \pi \frac 1 5 sin(5 \pi f_mx ) + \frac 4 \pi \frac 1 7 sin( 7 \pi f_mx)} ) $$
$f_c :$ carrier frequency
$f_m :$ frequency of the modulation
$A :$ amplitude
$I :$ impact of the modulation
$x :$ time
I tried to set up the formulas (on desmos) for a pulse modification and a graph, to validate what I should hear. But the graph does not look the way I expected. Is this from the acoustic perspective correct? Because I expected, that the low frequency area from the carrier signal would appear in the valley of the pulse.
Appendix, 09.06.2020: The formula for the frequency modulation, I got from an example, that modulates a sinus wave. And my intention was to replaced the sinus with a pulse wave. It was from an article from the American Mathematical Society webpage, looking like this:
$$y_m=A \cdot sin( 2 \pi f_c x + I \cdot \color{purple}{( sin( 2 \pi f_m x)})$$
The original pulse function I got from a desmos example and it was looking like this:
$$y_{s} =\color{green}{\frac4 \pi \frac 1 1 sin(1 \pi x) + \frac 4 \pi \frac 1 3 sin(3 \pi x) + \frac 4 \pi \frac 1 5 sin(5 \pi x ) + \frac 4 \pi \frac 1 7 sin( 7 \pi x)}$$
