Past exam of the physics A course of the University of Cambridge / 2016 / Paper 1 / Section D / D13 / c

Uniform signal sampling at rate $f_s$ multiplies a continuous signal by a time-domain Dirac comb, giving frequency-domain replicas spaced by $f_s$:If a baseband signal is restricted to $|f|\le B$ and $f_s>2B$, these replicas can be separated by an ideal reconstruction filter. Frequencies differing by integer multiples of $f_s$ have the same sampled phase progression; for real signals they fold into the interval from zero to $f_s/2$. This ambiguity is aliasing.

For example, $0.8f_s$ and $0.2f_s$ cosines produce identical sample values. Apply an analogue Anti-aliasing filter before digitization and choose enough sample-rate margin for its finite transition band. A digital filter applied afterward cannot distinguish components already folded onto one another. Out-of-band noise also aliases unless filtered. The sample rate sets temporal/spectral coverage; quantization resolution sets amplitude precision and is a separate limitation. Bandpass Signal sampling has additional conditions beyond the simple baseband rule.^[ref]