Math Bridge: Vibration Sampling Before Edge AI

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Math BridgeEdge & FogStruggle-friendly runway

Can a model recover a vibration the ADC has disguised?

Follow the chapter's pump signal through Nyquist, aliasing, ADC levels, and the noise floor delivered to inference.

Edge Eddie, the guideEdge Eddie guides
The one targetProve the pump input is honest before training.
The chapter case1200 Hz band, 2000 Hz example, ±4g 12-bit ADC.
What it buys youA sampling record the model cannot silently reinterpret.

A field team faces an unresolved physical question: Can a model recover a vibration the ADC has disguised? They must answer it before changing accelerometer sample rate in hertz on the real device. Predict the direction first.

See the relationship before changing it

The figure reads from left to right. The blue card is accelerometer sample rate in hertz. The middle card applies this page's relationship. The green card is band minimum. Walk the arrows once: set the input, apply the rule, then read the result with its unit.

The retained audit below checks several chapter fixtures. This added model holds every other chapter fixture fixed, so the numeric fixture does not switch without explanation.

Accelerometer sample rate in hertz changes band minimum An input card leads through the page relationship to the band minimum result. SET INPUT ONE CONTROL APPLY RULE predict calculate check units READ RESULT
Walk the arrows. Only the frequency outputs move because the control changes the clock, not the converter range or bit depth. That separation is the evidence.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline for accelerometer sample rate in hertz is 3200.

  2. 2

    Name the relationship. fNyquist=fs/2; falias=|fsignal-nfs|; q=FSR/2^N; qrms=q/√12

  3. 3

    Substitute the chapter fixture. Set accelerometer sample rate in hertz to 3200. The page ledger gives band minimum as 2400 Hz.

  4. 4

    Read the result. Keep Hz beside the value. Use it only inside the technical boundary on this page.

Predict, then change accelerometer sample rate in hertz

Try Predict the direction of band minimum. Move one control, calculate, then check your prediction.

3200
Chapter baseline
Band minimum

Observe Only the frequency outputs move because the control changes the clock, not the converter range or bit depth. That separation is the evidence. Reset the control to 3200 and compare band minimum.

Explain Only accelerometer sample rate in hertz moves here. The other chapter fixtures remain fixed.

Check yourself

What should you do before trusting a moved-control result?
Answer: Predict its direction, apply the shown relationship, keep the units, and reset to the worked baseline.
What does this small model leave out?
Answer: Only accelerometer sample rate in hertz moves. Field effects named in the page's technical boundary stay fixed.

Honesty note. This teaching model changes only accelerometer sample rate in hertz. It replays the chapter fixture; it is not a field prediction.

1. Separate time from amplitude

Sample rate decides which frequencies keep their identity. ADC bit depth decides how finely each amplitude is recorded. A later model can learn only the codes it receives; it cannot reconstruct a folded tone or remove the ADC's rounding floor.

Edge Eddie: Training quality begins at the sensor clock, not at the optimizer.

2. Name every algebra move

1

Double the band edgeThe minimum sample rate is 2fmax.

2

Choose the nearest spectral copySubtract n times the sample rate from the signal and take the magnitude.

3

Count ADC levelsN bits make 2^N codes.

4

Divide the full rangeq = FSR / 2^N.

5

Turn a uniform step into RMS noiseqrms = q / √12.

3. Work the pump numbers

fmin = 2(1200) = 2400 Hz; q = 8/4096 = 0.001953 g

At 1600 Hz, the 2000 Hz example lands at |2000 − 1600| = 400 Hz. At 12 bits, qrms = 0.000564 g and the ideal quantisation ceiling is 74.0 dB. The frequency and amplitude checks answer different questions.

4. Try one controlled change

fNyquist=fs/2; falias=|fsignal−nfs|; q=FSR/2^N; qrms=q/√12

TryMove only the accelerometer sample rate. The 1200 Hz fault band, 2000 Hz example, ±4g range, and 12-bit converter stay fixed.

Nyquist limit
Band minimum
2000 Hz appears at
ADC levels
ADC step
RMS floor
Ideal SNR
1200 Hz band cleared?

ObserveAt 3200 Hz the Nyquist limit is 1600 Hz, the 1200 Hz band clears, and the separate 2000 Hz example appears at 1200 Hz. At 1600 Hz that example aliases to 400 Hz and the band fails.

ExplainOnly the frequency outputs move because the control changes the clock, not the converter range or bit depth. That separation is the evidence.

Technical boundaries.

This is an ideal sampling and uniform-quantiser model.

Filter
A real anti-alias filter needs transition margin below Nyquist
ADC
Offset, nonlinearity, sensor noise, and clipping can exceed the ideal floor
Model
Passing these checks does not prove classification accuracy or drift tolerance

Use the actual sensor transfer function, output-data-rate mode, analogue filter, and field spectrum for release.

5. Do not merge the two quantisers

The sensor ADC rounds measured acceleration before training. INT8 model conversion rounds trained weights afterward. The same q/√12 pattern can describe both ideal rounding floors, but their units, ranges, and failure evidence are different.

6. Carry a defensible input record

Record the fault band, sensor range, output data rate, analogue filter, ADC bits, mounting, clipping rate, observed spectrum, preprocessing version, and model artifact that consumed those samples.

7. Check yourself

Why is 2400 Hz the bare minimum for a 1200 Hz band?
Answer: Nyquist requires at least twice the highest retained frequency.
Why can a 2000 Hz tone look like 400 Hz at 1600 samples/s?
Answer: Its nearest sampled spectral copy is |2000 − 1600| = 400 Hz.
Does 74.0 dB prove the deployed input has that SNR?
Answer: No. It is an ideal quantisation ceiling before sensor, analogue, timing, and environmental errors.
Honesty boundary.

The page preserves the chapter's catalog-typical teaching example without turning it into a pump specification.

1200 Hz
Teaching fault-band edge
±4g, 12 bit
Example converter range and depth
74.0 dB
Ideal quantisation ceiling only

Go deeper in the chapter, then measure the installed sensor path and representative faults.

Return to Edge AI & ML Fundamentals with the maths unpacked →