Rule of thumb · Control SystemsNº 69 / 167

Aliases fold around half the sample rate

A tone above fs/2 reappears mirrored below it — 900 Hz sampled at 1 kHz reads as 100 Hz.

Why it works

Frequencies reflect around the Nyquist frequency like a folded ruler. Anti-alias filters exist to remove them before the sampler ever sees them.

When it fails

Deliberately, this becomes a feature rather than a fault: undersampling folds a 2.4 GHz carrier down to something a slow converter can read, which is how direct-RF sampling receivers work. The fold is only a bug when you did not intend it.

Do it exactly

Estimate with the rule, then check it against the calculator that models it properly.

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What is aliasing and why does it happen?

A tone above fs/2 reappears mirrored below it — 900 Hz sampled at 1 kHz reads as 100 Hz. Frequencies reflect around the Nyquist frequency like a folded ruler.

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