Explain the Nyquist theorem and what happens when you violate it (aliasing).

The Nyquist-Shannon sampling theorem states that to perfectly reconstruct a continuous signal from discrete samples, the sampling rate must be at least twice the highest frequency component present in the signal: f_sample >= 2 * f_max. The frequency f_sample / 2 is called the Nyquist frequency — it is the upper boundary of signals that can be correctly represented at that sample rate.

When the sampling rate is too low, aliasing occurs: frequency components above the Nyquist frequency "fold back" into the representable spectrum and appear as false low-frequency signals that are mathematically indistinguishable from real ones. For a concrete example: sampling a 60 Hz signal at 100 Hz produces an alias at 40 Hz (|100 - 60| = 40). A 150 Hz signal sampled at 200 Hz aliases to 50 Hz. Once aliased, the false signal cannot be removed by any amount of digital filtering because it occupies the same frequency bin as a legitimate signal would. The data is permanently corrupted.

Prevention requires an anti-aliasing filter — an analog low-pass filter placed physically before the ADC input that attenuates all frequency components above the Nyquist frequency. This must be analog because digital filtering happens after sampling, which is too late. In practice, you should not sample at exactly 2x the signal bandwidth because that assumes a perfect brick-wall filter (infinite roll-off), which does not exist in analog electronics. Instead, sample at 5-10x the signal bandwidth to provide transition band for a practical filter. For example, if your signal of interest goes up to 1 kHz, sample at 5-10 kHz and use a simple 2nd-order RC filter with a -3 dB cutoff around 1.5-2 kHz. The excess sampling rate relaxes the filter requirements from an impractical brick wall to a gentle, inexpensive roll-off.