Privacy Priya guidesA field team faces an unresolved physical question: When does a Wi-Fi sample rate reveal walking motion? They must answer it before changing walk speed 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 walk speed. The middle card applies this page's relationship. The green card is wavelength. 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.
Derive the baseline in four named moves
- 1
Name the input. The chapter baseline for walk speed is 1.4.
- 2
Name the relationship. λ = 3.00x10⁸/(5.00x10⁹) = 0.0600 m walking fd = 2(1.40)/0.0600 = 46.7 Hz minimum sample rate = 93.3 Hz breathing fd = 0.628 Hz
- 3
Substitute the chapter fixture. Set walk speed to 1.4. The page ledger gives wavelength as 0.060 m.
- 4
Read the result. Keep m beside the value. Use it only inside the technical boundary on this page.
Predict, then change walk speed
Try Predict the direction of wavelength. Move one control, calculate, then check your prediction.
Observe Rate limiting can remove reconstructable gait detail, but aliases can still look like slower motion and must be tested. Reset the control to 1.4 and compare wavelength.
Explain Only walk speed moves here. The other chapter fixtures remain fixed.
Check yourself
What should you do before trusting a moved-control result?
What does this small model leave out?
1. See the body as a changing path
A receiver adds the direct radio path to reflections. When a person moves, one reflected path changes length. Its phase then changes over time, which appears as a Doppler frequency in CSI or RSSI measurements.
2. Name every algebra move
Find wavelengthλ=c/f.
Project velocityMultiply v by cos(θ).
Count the return pathfd=2v cos(θ)/λ.
Double for Nyquistfsample≥2fd.
3. Reproduce walking and breathing
walking fd = 2(1.40)/0.0600 = 46.7 Hz
minimum sample rate = 93.3 Hz
breathing fd = 0.628 Hz
A 100 Hz capture has only a 7.14% margin. Sampling at 10 Hz is 9.33× too slow for that walk and folds that motion to about 3.33 Hz.
4. Try the walking speed
TryMove radial speed and compare the required sample rate with 100 Hz capture and a 10 Hz limit.
ObserveFaster radial motion raises Doppler and the honest sampling minimum in direct proportion.
ExplainRate limiting can remove reconstructable gait detail, but aliases can still look like slower motion and must be tested.
The model follows one reflection moving along the link axis.
- Geometry
- Sideways motion reduces the cos(θ) term
- Room
- Real multipath produces several Doppler components
- Receiver
- Noise, quantisation, packets, and algorithms set detection limits
Verify the actual hardware and processing pipeline with consent-safe trials.
5. Turn maths into minimisation
Choose the lowest measurement rate and precision that still support the declared product action. Test whether gait, breathing, presence, or identity clues remain recoverable rather than assuming a lower number is private.
6. Record the privacy boundary
Record carrier, sample rate, resolution, retention, local versus remote processing, outputs, access, consent state, bystander exposure, and tests showing what motion can and cannot be inferred.
7. Check yourself
Why is walking about 46.7 Hz here?
Why is 100 Hz only just enough?
Does 10 Hz guarantee no motion inference?
The chapter names the privacy control; the band, rates, walk, and breathing motion are explicit teaching assumptions.
- 5 GHz and 1.40 m/s
- Worked sensing case
- 100 Hz and 10 Hz
- Compared capture policies
- 1 cm at 0.300 Hz
- Breathing illustration
Correct, not complete: this Doppler ledger does not prove privacy, consent, identity protection, or detector performance.