Sampling and aliasing of a signal

Question

I'm given the signal $x(t)=\cos(100*\pi*t)+\cos(200*\pi*t)+\sin(500*\pi*t)$ and I need to find the least sampling frequency in order to reconstruct the $x(t)$ signal from the following of it's samples.

Any thoughts?

Answer 1

You need a sampling frequency that is at least twice the largest frequency present in your signal. In your case, $$\omega_{max} = 500\pi \implies f_{max}=\frac{\omega_{max}}{2\pi}=250\text{Hz} $$

Which means that,

$$\boxed{f_{sampling} \geq 2f_{max} = 500\text{Hz}}$$