Sampling
Đã giới thiệu| English | Ý nghĩa |
|---|---|
| Nyquist criterion | tiêu chuẩn Nyquist |
| aliasing/ˈeɪlɪəsɪŋ/ | hiện tượng chồng chập tần số |
| anti-alias filter | bộ lọc chống trói |
| guard band | guard band |
Replicas at every multiple
- Sampling multiplies by an impulse train; the spectrum replicates at multiples of $f_{s}$. The Nyquist criterion: $f_{s} > 2f_{max}$ or replicas overlap and aliasing folds highs into false lows.
4 kHz sampled at 6 kHz IS a 2 kHz sequence: $\cos(2\pi\cdot\tfrac{2}{3}n) = \cos(2\pi\cdot\tfrac{1}{3}n)$ sample by sample ✓.
{exercise:uni-ee0641-alias}
A 5 kHz tone sampled at 8 kHz appears as —
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5 > 8/2 = 4, so it aliases to |5 − 8| = 3 kHz. Always fold around fs/2.
The filter goes before
- The anti-alias filter must cut everything above $f_{s}/2$ BEFORE the sampler: a folded frequency carries no flag of where it came from. The guard band between $f_{max}$ and $f_{s}/2$ is the design budget.
{exercise:uni-ee0642-guard}
With content to 20 kHz sampled at 44.1 kHz, a 23 kHz interference tone lands at —
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44.1 − 23 = 21.1 kHz — inside the audio band. The guard band is only 2.05 kHz, which is why pro capture oversamples.
The anti-alias filter belongs —
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Once folded, a frequency carries no flag of where it came from — no filter after the sampler can undo the fold.