Nyquist Sampling Theorem
See how sample rate controls aliasing, reconstruction, and sensor data quality
Nyquist Sampling Theorem
Watch a continuous signal become ADC samples. When the sample rate is too low, the same dots can fit a slower false wave, so the digital system sees an alias instead of the original signal.
Sampling and Reconstruction
The sample dots are the only information the digital system receives.
Learning Support
Samples are evidence
The ADC does not keep the smooth analog wave. It keeps individual points. If those points are too sparse, multiple waves can explain the same evidence.
Nyquist is a minimum
The theoretical minimum is twice the highest signal frequency. Real systems normally add guard margin because filters, phase, and sensor uncertainty are not ideal.
Aliasing is permanent
Once a high frequency folds into a low false frequency during sampling, ordinary digital processing cannot know which one was real.
Filter before sampling
An anti-alias filter must be analog and before the ADC. It removes frequencies above the Nyquist frequency before they can fold into the sample data.
Quick Reference
Nyquist frequency
f_nyquist = sample_rate / 2
This is the highest signal frequency that can be represented without aliasing in the ideal model.
Minimum sample rate
sample_rate >= 2 x f_signal_max
Use this as the teaching minimum, then add practical margin for real sensors and filters.
Alias frequency
f_alias = abs(f - round(f / fs) x fs)
Fold the result into the 0 to fs/2 band. Example: 18 Hz at 25 samples/s appears as 7 Hz.
Borderline case
sample_rate = 2 x f_signal
This touches the mathematical boundary. Phase and real-world imperfections make it a poor design target.
Temperature sensors
slow signal -> low sample rate is usually fine
Slow environmental signals often need only modest sampling, but the sensor bandwidth still matters.
Vibration sensors
fast signal -> high sample rate
A 1 kHz vibration feature needs at least 2 k samples/s, often more with guard margin.
Power trade-off
more samples -> more energy and data
Sampling faster can improve fidelity, but it may increase ADC energy, processing, storage, and radio traffic.
Anti-alias filter
low-pass before ADC
The filter limits incoming analog bandwidth so the ADC never sees frequencies it cannot represent.