Periodization (of a spectrum)

The tiling effect sampling in time has on a signal's spectrum in frequency.

Sampling $f$ in time periodizes $\hat f$ in frequency: it tiles infinitely many shifted copies of the original spectrum, spaced $\omega_s$ (the sampling angular frequency) apart, and adds them together. Aliasing is exactly what happens when those tiled copies overlap.

Examples

Sampling at too low a rate periodizes the spectrum densely enough that neighboring copies overlap, causing aliasing.