- 2069 Asar · 2 marks
Why band-limit a signal before sampling
Short answer
To prevent aliasing, where frequency components above half the sampling rate fold into the baseband and corrupt the signal, a low-pass anti-aliasing filter must limit the signal band below the Nyquist frequency. This ensures the sampling theorem condition fs ≥ 2fmax is satisfied.
Why is it necessary to limit the band of a signal before performing sampling?
Sampling a signal at rate fs repeats its spectrum around every multiple of fs. If the signal has frequency components above fs/2, the repeated spectra overlap and the original signal cannot be recovered. This distortion is called aliasing.
- Nyquist theorem: no aliasing only if fs ≥ 2 fmax.
- Real signals (speech, noise) contain components well above the band of interest, and fs cannot be made infinite.
- So the signal is first passed through a low-pass anti-aliasing filter that removes everything above fs/2. The signal is then truly band-limited and the sampling theorem holds.
Example: a telephone voice channel is filtered to about 4 kHz before sampling at 8000 samples/s. Without the filter, 6 kHz noise would alias to 2 kHz and appear as false audio in the speech.
✓ Answer checked by Claude Sonnet 5.5
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