# Sampling - Higher order harmonics

I have been studying about the sampling theorem and it seems that even though we sample at a frequency with the nyquist criterion, the harmonics (due to sampling process) remain within the nyquist frequency range, as illustrated below:

If we sample a 5MHz sine wave with 20 MHz sampling frequency (nyquist frequency being 10 MHz), its fundamental and harmonic frequencies (up to 4th) lie at:

fin=5 MHz (fundamental)

1st Harmonics: (around fs) fs+fin=25 MHz fs-fin=15 MHz

2nd Harmonics: (outside nyquist) fs+(2*fin)=30 MHz fs-(2*fin)=10 MHz

3rd Harmonics: fs+(3*fin)=35 MHz fs-(3*fin)=5 MHz (Inside nyquist)

4th Harmonics: fs+(4*fin)=40 MHz fs-(4*fin)=0 (DC)

I understand that when doing a high level simulation in matlab, we do windowing or coherent sampling to overcome this harmonics falling into the nyquist range or signal band by choosing a prime number of cycles.

But practically, if we give an arbitrary frequency to an ADC, which usually has a sample/hold circuitry in the front, aren't these harmonics generated by it?

Or do we have the control of the harmonics' power so that we can adjust it to a minimum (depending on the application).

(This question also relates to my previous question - Higher order harmonics during sampling)