Different continuous patterns can produce the same discrete samples. When that happens, the sampled data cannot determine which original pattern was present; the patterns are aliases of one another.

Aliasing occurs when the sampling grid is too coarse for the variation being represented. A rapidly oscillating waveform can appear to have a lower frequency, and fine stripes in an image can become false wider bands or moiré patterns.

The information is already lost at sampling time. Enlarging, smoothing or otherwise processing the stored samples afterward cannot uniquely recover detail that never affected the samples.

Avoiding aliasing therefore requires controlling what reaches the sampler. One can increase sampling density, remove variation finer than the grid can represent, or average over the sample's finite area instead of taking an ideal point value.

Frequency-domain sampling theorems make these limits precise for band-limited signals, but the underlying problem is more general: discrete samples cannot preserve arbitrary variation between sample locations.