aliasing

In old Western films a fast-spinning wagon wheel sometimes appears to turn slowly backwards. The film captures only 24 frames a second, and between frames the wheel rotates almost a full spoke-spacing, so your eye reads it as a small reverse step. The wheel's true fast spin has put on a disguise — a slow backward alias. Aliasing is exactly this: when you sample a signal too sparsely, frequencies too high to be resolved masquerade as lower frequencies that you cannot tell apart from the real thing.

Sampling at a rate of f_s samples per second can faithfully represent oscillations only up to f_s / 2, the Nyquist frequency. Any genuine frequency f above that gets FOLDED down: it appears in your data at the alias frequency |f - k*f_s| for whichever integer k brings it into the range 0 to f_s/2. A 30 Hz tone sampled at 50 Hz, for instance, folds to |30 - 50| = 20 Hz and is forever indistinguishable from a true 20 Hz tone in those samples. The information has not been corrupted so much as confused: two different continuous signals produce literally the same sample values, so no algorithm — not the DFT, not the FFT, nothing — can untangle them after the fact.

The cure is to remove the offending high frequencies BEFORE sampling, with an analog anti-aliasing low-pass filter, or to sample fast enough that nothing real lives above Nyquist. This is why audio is sampled at 44.1 kHz (comfortably above twice the roughly 20 kHz limit of human hearing) and why camera and graphics pipelines blur or supersample to avoid jagged, shimmering edges. The honest, slightly uncomfortable truth is that aliasing is irreversible: once high frequencies have folded into your samples, they are permanently disguised as lower ones.