A signal can be reconstructed only if sampled above twice its highest frequency

The Nyquist–Shannon sampling theorem states that a continuous signal can be sampled and perfectly reconstructed only if the sampling rate exceeds twice the highest frequency present in the signal. Half the sampling rate is the Nyquist frequency — the ceiling above which components cannot be faithfully represented; equivalently, at least two samples per period are needed to capture a sine. Frequencies above Nyquist do not simply disappear: they alias, folding back and appearing as false lower frequencies in the audible range. To prevent this, an analog anti-aliasing low-pass filter removes energy above Nyquist before the ADC, and the DAC uses a reconstruction low-pass to rebuild a smooth signal from the discrete samples; modern converters also use oversampling plus digital low-pass. CD audio samples at 44.1 kHz (Nyquist 22.05 kHz), a small margin above 2×20 kHz to allow a practical filter roll-off, comfortably covering human hearing. A common mistake is thinking the theorem applies only to sine waves — it applies to every spectral component of any complex signal. (Separately, bit depth sets dynamic range: about 6 dB per bit, so 16-bit gives roughly 96 dB.)

Examples

Sr = 48 kHz → Nyquist 24 kHz; a 30 kHz tone aliases to (48000 − 30000) = 18 kHz, an audible artefact. Sr = 44.1 kHz → Nyquist 22.05 kHz; a 20 kHz tone is safely below it, but a 25 kHz tone aliases to 19.1 kHz. DVD audio at up to 192 kHz can represent up to 96 kHz.

Assessment

Given a 48 kHz sampling rate, state the Nyquist frequency and the frequency a 30 kHz component would alias to. Explain why the ADC must include a low-pass filter, and why the theorem is not limited to sine waves. How does bit depth relate to dynamic range?