Solution (source code)

= Solution

Sampling at $t_n=n/f_s$ makes a <frequency> $f$ indistinguishable from $f+kf_s$, since the extra phase is $2\pi kn$. For a real <sinusoid>, reflection to $|kf_s-f|$ also gives an alias, up to phase. For example, a $50\,\mathrm{Hz}$ cosine sampled at $80\,\mathrm{Hz}$ has exactly the samples of a $30\,\mathrm{Hz}$ cosine. A measured low-frequency feature can therefore originate above the instrument's <Nyquist frequency>.

To reconstruct an arbitrary baseband <signal> limited to <bandwidth> $B$, sample strictly above $2B$ and use an analogue <anti-aliasing filter> before the sampler. A practical filter needs a transition band, so merely choosing a nominal rate $2B$ is insufficient. <frequency> components already folded together cannot in general be separated by later digital filtering. <aliasing> from insufficient sampling is distinct from <spectral leakage> caused by a finite observation window.