A signal \(x(t)=\cos(2\pi \cdot 9t)\) is sampled at \(f_s = 12\,\text{Hz}\) and then reconstructed with an ideal low-pass filter with cutoff \(6\,\text{Hz}\). What is the frequency of the reconstructed signal?
After sampling, 9 Hz folds to \(|9-12| = 3\,\text{Hz}\), which lies inside the cutoff, so the filter keeps 3 Hz. Leaving 9 Hz unfolded ignores that reconstruction only sees the apparent frequency.
Aliasing is the overlap of spectral replicas that occurs when a signal is sampled at a rate below twice its bandwidth, so that different frequencies become indistinguishable from one another.
\[f_{\text{alias}} = |f - k\,f_s|, \quad k \in \mathbb{Z}\]