Signal-processing project
Đã giới thiệu| English | Ý nghĩa |
|---|---|
| resolution/ˌrezəˈluːʃn/ | độ phân giải |
| processing gain | processing gain |
The specification bites first
- Build the tone detector as verified stages: anti-alias filter → window → FFT → threshold. A bin resolution of 1 Hz at $f_s = 1$ kHz needs $N \ge 1000$ — already 1.0 s of data against a "<1 s latency" spec: the conflict surfaces at design time, and the margin table records the trade.
$N = 1024$: 0.977 Hz ✓ but a 1.024 s record ✗; $N = 1000$: 1.000 Hz, exactly on the line. Nothing silent.
{exercise:uni-ee1207-spec}
At fs = 1 kHz the "1 Hz bins, under 1 s latency" spec pair —
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Δf = fs/N makes 1 Hz cost exactly 1 s of samples — the conflict is arithmetic, and surfacing it at design time is the point of the spec.
The gain that decides feasibility
- Coherent energy lands in one bin while noise spreads over $N/2$: processing gain $10\log_{10}(N/2)$ — 27 dB at $N = 1024$. A $-10$ dB SNR tone becomes $+17$ dB in the decision bin ✓ — detectable before anything is built.
{exercise:uni-ee1207-gain} {exercise:uni-ee1207-report}
The bin processing gain of an N = 1024 FFT is about —
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The tone's energy lands in one bin while noise spreads over N/2 = 512 bins: 10log10(512) = 27.1 dB of separation.
A project report that meets 5 of 6 specs and says so is —
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Measured margins with no silent goals are the deliverable; the honest table is the engineering.