Ada Audits the Lab Numbers
Ada checks sample-rate margin, ADC step size, and spectral resolution before a lab trace is release evidence
ADA · CALCULATION AUDIT
Ada Audits the Lab Numbers
A clean lab trace is only trustworthy when the arithmetic proves the capture could preserve the physical event before any smoothing or downsampling makes the display look calm.
A vibration lab expects useful energy up to 1 kHz and needs to see amplitude changes as small as 1 mV, so the team tests sample rates of 3.2 kHz and 4 kHz against the Nyquist minimum and checks an 8-bit ADC against a 12-bit ADC at a 3.3 V reference. This audit asks the question that setup invites: does the chosen sample-rate margin and ADC bit depth actually preserve a 1 mV event, or does the 8-bit plan fail on arithmetic alone?
Companion to the chapter Lab: Signal Processing — every number here comes from that chapter.
1. Timing evidence starts from Nyquist, then adds margin
The chapter's vibration example names useful energy up to 1 kHz. The lower mathematical boundary is just the starting line:
3.2 kHz / 2 kHz = 1.6 x minimum
4.0 kHz / 2 kHz = 2.0 x minimum
2. ADC resolution is a voltage-step test, not a bit-count boast
With a 3.3 V reference, the code step is the reference divided by the available codes:
12-bit step = 3.3 V / 4096 = 0.000805664 V = 0.806 mV
16-bit step = 3.3 V / 65536 = 0.000050354 V = 0.050 mV
3. A 1 mV requirement rejects the 8-bit plan on arithmetic alone
The smallest meaningful change is smaller than one 8-bit code, but larger than one 12-bit code:
1 mV / 0.806 mV = 1.24 codes
1 mV / 0.050 mV = 19.9 codes
4. Frequency evidence needs the record length
The chapter's FFT rule stays symbolic until the lab records both sample rate and sample count:
At fs = 4 kHz: bin spacing = 4000 / N Hz
What the audit buys you: the lab can defend a sample-rate choice, reject a converter that cannot resolve the physical change, and explain why frequency claims need the captured record length before the result is release evidence.
Every number above is taken from this chapter's own worked example and re-derived step by step.