Electronics & Circuits · Study deck
Sampling and Aliasing: Nyquist and Filters
A sensor can report a slow false wave when it samples a fast real signal.
Voltage Vera is your guide for this deck.
After studying this chapter
Learning objectives
You will be able to:
- Apply Nyquist Theorem: Calculate minimum sampling rates for different signals
- Diagnose Aliasing: Explain why undersampling causes incorrect frequency representation and predict aliased frequencies
- Design Anti-Aliasing Filters: Specify hardware low-pass filter parameters to prevent high-frequency contamination before ADC
- Evaluate Sampling-Power Trade-offs: Select optimal sampling rates that satisfy Nyquist while minimizing energy consumption in battery-powered IoT devices
Major section
Start Simple
Nyquist sampling is the rule that prevents a changing signal from pretending to be something else.
- The stored trace may be neat and still be false.
- Sampling rate means how many measurements are taken each second.
- The deeper sections develop aliasing, limits, filtering, oversampling, and reconstruction.
Major section
Deep dive: Putting Numbers to It
For audio sampling human voice (max frequency $f_{max} = 3400$ Hz), Nyquist requires $f_{sample} \geq 2 \times 3400 = 6800$ Hz minimum.
- Telephony uses 8 kHz (18% margin).
- That reading provides the evidence needed for the section’s next calculation, comparison, or field check.
- Following those roles reveals how sample rate changes the reconstructed signal.
Major section
Deep dive: Putting Numbers to It (continued)
The theorem has direct implications for how we choose sampling rates in practice.
- Bare Nyquist is the mathematical minimum, but real devices usually need extra margin for noise, timing uncertainty, and anti-aliasing filter roll-off.
- It turns how sample rate changes the reconstructed signal from a verbal claim into labelled evidence.
- Undersampling (too slow) causes aliasing - high frequencies appear as low frequencies!
Major section
Sampling Tradeoffs for Vibration
Option A: 500 Hz Sampling (FAILS).
- Sampling at 500 Hz = exactly at signal frequency → aliasing occurs!
- Aliasing:: Nyquist frequency is only 250 Hz, so the 500 Hz component folds back to |500: 500| = 0 Hz (DC) or nearby low frequencies depending on phase.
- But:: Real motors have frequency components >500 Hz (harmonics, noise).
Deck summary
Key takeaways
Nyquist sampling is the rule that prevents a changing signal from pretending to be something else.
- For audio sampling human voice (max frequency $f_{max} = 3400$ Hz), Nyquist requires $f_{sample} \geq 2 \times 3400 = 6800$ Hz minimum.
- The theorem has direct implications for how we choose sampling rates in practice.
- Option A: 500 Hz Sampling (FAILS).
Retrieval practice
Recall check
Voltage Vera says: answer from memory, then check your reasoning.
Q1You need to sample a 500 Hz signal. What is the minimum sampling rate according to Nyquist?
Show answer
Answer: C The Nyquist theorem requires f_sample >= 2 x f_max = 2 x 500 Hz = 1000 Hz.
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Answers
Answer key.
- C · The Nyquist theorem requires f_sample >= 2 x f_max = 2 x 500 Hz = 1000 Hz.