How it works
When a signal of frequency f is sampled at rate f_s < 2f, the aliases appear at frequencies |f − k·f_s| for integer k. The apparent frequency of the aliased component is f_alias = |f mod f_s| when f mod f_s ≤ f_s/2, or f_s − (f mod f_s) when f mod f_s > f_s/2. Graphically, aliasing appears as spectral copies of X(f) shifted by multiples of f_s overlapping with the baseband copy, making it impossible to separate the original signal component from the alias using any filter applied after sampling.
Key points to remember
Aliasing is irreversible once it occurs — no post-processing can recover the original signal. The solution is always applied before the ADC: an anti-aliasing low-pass filter with sharp cutoff at f_s/2 removes frequency components that would alias. For a 44.1 kHz audio system, the anti-aliasing filter must attenuate all content above 22.05 kHz. Temporal aliasing occurs in video when a wheel appears to spin backwards under strobe lighting: the rotational frequency exceeds half the frame rate. Spatial aliasing appears in images sampled below the Nyquist spatial frequency, causing moiré patterns. Both are the same phenomenon, just in different domains.
Exam tip
The examiner always asks you to calculate the alias frequency of a given signal sampled below the Nyquist rate — show the folding calculation step by step and draw the overlapping spectra to earn full marks.