The following signal $$ f(t) = 2\cos(20 \pi t) + 3\cos(80 \pi t) + 4\cos(200 \pi t) $$ is sampled at a frequency $F_s = 100\text{ Hz}$, then it is reconstructed using an ideal lowpass filter (no frequency given). I am asked to determine the signal coming out of the reconstruction filter.
By my understanding on ideal filters, a cutoff frequency of $ 100\text{ Hz}$ should be enough (since the signal has $ F_{max} = 100 \text{ Hz}) $.
So the result that I am expecting is the same that I started with, however the result that I am given is:
$$ f(t) = 4 + 2\cos(20 \pi t) + 3\cos(80 \pi t) $$
Why is it that there's no $\cos(200 \pi t)$ and there's only a $4$?
If the sampling frequency is $ F_s = 100$ Hz, the maximum frequency you can "capture" is 50 Hz. The last term $ 4 cos (200 \pi t) = 4 cos (2\pi t \cdot 100) $ is therefore rejected.