I'm interested in developing audio software. I've read the books by Will Pirkle and there's something I'm struggling to understand about how non-linear functions affect the frequency spectrum of a signal. Particularly I'm concerned about avoiding aliasing noise.
In his book, Pirkle points out the problem: harmonics are created by non-linear functions (e.g. clipping/rectifiers, etc) and those harmonics, in principle, extend upwards past the Nyquist frequency, causing aliasing. The only solution offered is an oversampling->LPF->decimation pipeline, which is easy to understand. If you oversample by 4x then you should only get aliasing from the harmonics that are past 4x the original Nyquist frequency (which is hopefully very low energy by that point).
What I'm wondering though is: is there any way to calculate the rate at which the harmonics decrease in power for a given function (other than actually evaluating the function on a test signal and doing an FFT)? The idea is if you could compute this, maybe you could set the oversample rate adaptively.