# Magnitude of intermodulation distortion products?

Assuming I have a set of frequencies $\mathbf F$, and I pick 2 frequencies $f_1$ and $f_2$ randomly from the set, generate sine waves for them, and pass the signals through a non-linear distortion process while adding them.

• Is there any way for the harmonics or intermodulation distortion products to have a magnitude larger than the magnitude of any of the two frequencies, when calculating an FFT?
• If yes, under what conditions, and how can I avoid that this happens?

Example: If the system is a squarer that produces output $x^2(t)$, then with $x(t) = \cos(2\pi f_c t)$, the output is entirely the second harmonic (and a DC term). Since the fundamental is entirely absent from the output, the harmonic amplitude is infinitely larger than the fundamental. If two sinusoidal inputs of frequencies $f_1$ and $f_2$ are added together before the squaring operation, then the output has second harmonics at frequencies $2f_1$ and $2f_2$, intermodulation distortion products at frequencies $f_1+f_2$ and $|f_1-f_2|$ and no fundamentals at frequencies $f_1$ and $f_2$.