Aliasing

Two different frequencies producing the identical sample sequence at a given sampling rate.

Aliasing is the collision of two different frequencies sharing one sample sequence at a given rate $f_s$ : every frequency $f$ has infinitely many aliases, $\{kf_s\pm f: k\in\mathbb Z\}$ . The one lying in $[0,f_s/2]$ , the apparent frequency, is what any reconstruction built purely from the samples will actually produce.

Examples

Sampling a $7$ Hz signal at $f_s=8$ Hz per second gives the identical samples a $1$ Hz signal would, since $7=8-1$ .