Take a sine wave below your system's Nyquist frequency. Chop off the top. Take the continuous Fourier transform. You will notice that there are now frequency components above the Nyquist limit of your system. Those will now be aliased down to lower frequencies.
One trick for doing nonlinear waveshaping without introducing too much aliasing is to perform the wave shaping at a higher sample rate than the rest of your system and then downsampling with a low pass filter. Thankfully, the high frequency components introduced by nonlinearity tend to decrease in magnitude reasonably quickly.
