In the following, we simulate the sample theory on an anolog signal: $y=0.5 \sin(2\pi f_1 t)+2\sin(2\pi f_2 t)$, whose frequece is $f_1=15$ and $f_2=40$.
We select $f_s=3f_{max}=3\times 40=120Hz$. We can compute $f_s-f_1=120-15=105Hz, f_s-f_2=120-40=80Hz$, together with $f_1=15Hz$ and $f_2=40Hz$, we should see four peaks, at $\omega=15, 40, 80, 105Hz$, in the frequency domain.
The results are shown in the follwing figure.
[code]
https://files.cnblogs.com/files/mathlife/samplingtheorem.rar