Eddie guidesA technician must decide whether nyquist frequency is safe before changing sample rate on the real device. The result is unresolved until the rule and units are checked. Predict the direction first.
See the relationship before changing it
The figure reads from left to right. The blue card is sample rate. The middle card applies this page's rule. The green card is nyquist frequency. 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 model keeps those stated values fixed and changes only sample rate, so the numeric fixture does not switch without explanation.
Derive the baseline in four named moves
- 1
Name the input. The chapter baseline is 1000 samples/s.
- 2
Name the relationship. vibration Nyquist = sample rate / 2
- 3
Substitute with units. 1,000 / 2 = 500 Hz
- 4
Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.
Predict, then change sample rate
Try Predict the direction of vibration Nyquist = sample rate / 2. Test another sample rate, then compare nyquist frequency.
Observe Raising sample rate lifts the Nyquist ceiling for the fixed vibration. Reset sample rate to 1000 and compare nyquist frequency.
Explain Raising sample rate lifts the Nyquist ceiling for the fixed vibration.
Check yourself
What should you do before trusting a moved-control result?
What does this small model leave out?
1. Start with the physical story
Sampling makes regular snapshots. If they arrive too slowly, several different wave motions can pass through the same sample points and become indistinguishable.
2. Name every algebra move
Turn rate into spacingThe interval is 1/fs seconds.
Mark the digital ceilingNyquist frequency is fs/2.
Test a band edgeRequire fs to be at least 2fmax.
Fold an over-limit toneSubtract the nearest whole sample-rate multiple.
Keep the filter before samplingAfter folding, the false and real low tone share one digital frequency.
3. Reproduce the chapter case
800 Hz is above that ceiling
alias=|800−1(1000)|=200 Hz
500 Hz defect margin=1000/[2(500)]=1.00
2500 Hz gives Nyquist=1250 Hz
The arithmetic stays visible so that units and assumptions can be checked before the result is used.
4. Try one real input
TryMove the sample rate. Watch the 800 Hz component fold, then become directly representable.
ObserveAt 1000 samples/s, 800 Hz appears at 200 Hz. At 2500 samples/s, Nyquist is 1250 Hz and the named 1 kHz precursor fits.
ExplainThe fold is not a warning flag in stored data. An analogue anti-alias filter must remove unwanted above-limit energy before the ADC.
This transparent ledger reproduces the named chapter case.
- Band
- The ledger uses three named tones, not an arbitrary continuous spectrum.
- Filter
- It does not model analogue filter order, roll-off, attenuation, or phase.
- Clock
- Jitter and sample-clock error are not included.
Correct, not complete: this ledger does not design an anti-alias filter or qualify a sampling chain.
5. Use the result in the design
Choose a sample rate above twice the useful band edge, then leave transition space for a real anti-alias filter instead of treating equality as generous margin.
6. Record the evidence state
Record useful bandwidth, interfering bands, sample-clock tolerance, analogue filter response, sample rate, and alias tests.
7. Check yourself
Why is 1000 samples/s only the boundary for 500 Hz?
Can software separate an aliased 800 Hz tone from a real 200 Hz tone?
Does a higher sample rate remove every error?
This transparent ledger reproduces the named chapter case.
- Band
- The ledger uses three named tones, not an arbitrary continuous spectrum.
- Filter
- It does not model analogue filter order, roll-off, attenuation, or phase.
- Clock
- Jitter and sample-clock error are not included.
Correct, not complete: this ledger does not design an anti-alias filter or qualify a sampling chain.