AI Tutor
Have you ever watched video footage of a fast-spinning helicopter blade where the rotor looks like it is creeping backwards or standing completely motionless in midair?
That optical illusion is called the wagon-wheel effect, and in scientific research, it represents one of the easiest ways to corrupt digital sensor measurements.

Continuous Physics to Discrete Numbers

Physical phenomena like heat diffusion, sound waves, and impact forces produce an analog signal — a seamless, continuous voltage that varies infinitely over time.
To log these measurements on a computer, an Analog-to-Digital Converter (ADC) takes periodic snapshots of that voltage at a fixed rate called the sampling frequency (fsf_s), measured in samples per second or Hertz (Hz\text{Hz}).
What determines whether those discrete red dots actually preserve the true physical behavior of our continuous wave?

The Nyquist-Shannon Criterion

In 1928, telecommunications engineer Harry Nyquist investigated telegraph transmission speeds, which mathematician Claude Shannon later formalized in 1949 into the Nyquist-Shannon Sampling Theorem.
The theorem states that to unambiguously reconstruct a signal containing frequencies up to fmax⁡f_{\max}, your sampling frequency must strictly satisfy fs>2fmax⁡f_s > 2 f_{\max}.
The half-sampling boundary fN=fs/2f_N = f_s / 2 is called the Nyquist frequency, and it represents the absolute highest frequency your digitizer can accurately represent.
When you sample slower than 2fmax⁡2 f_{\max}, high frequencies masquerade as false low frequencies in a phenomenon called aliasing.