Say I have an initial sine wave of frequency $F$ as such:
$$A=\sin(2\pi Ft)$$
And I can "saturate" that wave by adding waves close in frequency, then divide by the number of waves to roughly regulate the amplitude:
$$A=\frac{\sin(2\pi Ft)+\sin(2\pi (F+0.1)t)+\sin(2\pi (F-0.1)t)}{3}$$
I believe I should be able to build an integral that represents this for a CONTINUOUS range of values surrounding $F$, then solve that integral into a relatively simple equation. But my calculus days are too far gone now to know how to do this. I can tell I'm way off, but the closest my knowledge and research has gotten me is this:
$$A=\int_{-s}^s \frac{\sin(2\pi (F+x)t)}{\text{?}} \, dx$$
Am I close? Is this even possible?