Data Dora guidesA field team faces an unresolved physical question: Why can a 16 kHz audio pipeline turn ultrasound into an audible feature? They must answer it before changing tone 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 tone. The middle card applies this page's relationship. The green card is nyquist ceiling. 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 tone is 20000.
- 2
Name the relationship. 16,000/2 = 8,000 Hz 16,000x0.025 = 400 samples; 16,000x0.010 = 160 samples floor((16,000-400)/160)+1 = 98 frames/s 20,000 Hz → |20,000-16,000| = 4,000 Hz; 16 bit → 98.1 dB
- 3
Substitute the chapter fixture. Set tone to 20000. The page ledger gives nyquist ceiling as 8.0 kHz.
- 4
Read the result. Keep kHz beside the value. Use it only inside the technical boundary on this page.
Predict, then change tone
Try Predict the direction of nyquist ceiling. Move one control, calculate, then check your prediction.
Observe Aliasing creates plausible evidence at the wrong frequency, so metadata must bind sample rate to the model. Reset the control to 20000 and compare nyquist ceiling.
Explain Only tone 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. Start with the clock
A sample is one timed measurement. The sample clock decides which frequencies can be distinguished before an FFT or MFCC exists.
2. Name every algebra move
Halve the rateNyquist ceiling = fs/2.
Multiply by timesamples = fs × seconds.
Fold to the nearest copyfalias = |f − round(f/fs)fs|.
Count ideal converter rangeSNR = 6.02N + 1.76.
3. Reproduce the chapter
16,000×0.025 = 400 samples; 16,000×0.010 = 160 samples
floor((16,000−400)/160)+1 = 98 frames/s
20,000 Hz → |20,000−16,000| = 4,000 Hz; 16 bit → 98.1 dB
The 18, 20, and 22 kHz examples fold to 2, 4, and 6 kHz.
4. Try an emitted tone
TryMove the sensing tone through 18–22 kHz.
ObserveThe feature schedule stays fixed while the false in-band alias moves.
ExplainAliasing creates plausible evidence at the wrong frequency, so metadata must bind sample rate to the model.
This engine treats tones and an ideal converter.
- Clock
- No jitter or analogue filter response
- Signal
- No broadband noise or microphone response
- MFCC
- No window leakage or mel-filter loss
Measure the complete microphone and feature pipeline.
5. Separate the use cases
Speech and ultrasonic interaction need different acquisition contracts even when both end in compact features.
6. Record what travels
Version sample rate, frame, hop, bit depth, filter, window, FFT, mel bank, model, and threshold together.
7. Check yourself
What is the 16 kHz Nyquist ceiling?
Where does 20 kHz fold?
Does 98.1 dB prove the microphone is that quiet?
The chapter owns the digital schedule; the tone is its separate sensing example.
- 16 kHz, 25 ms, 10 ms
- Chapter keyword pipeline
- 18–22 kHz
- Chapter ultrasonic interaction band
- 98.1 dB
- Ideal PCM relation
Correct, not complete: this arithmetic does not qualify an audio detector.