Nyquist: freq máx de amostragem

Nyquist frequency: the highest signal a sample rate can represent

The Nyquist frequency is just half the sample rate: f_max = fs / 2. So a CD at 44.1 kHz tops out at 22.05 kHz, sitting a hair above the roughly 20 kHz ceiling of human hearing. Pro audio at 48 kHz reaches 24 kHz, and 96 kHz hi-res goes up to 48 kHz, grabbing ultrasonic harmonics along the way. According to the Shannon-Nyquist sampling theorem (1949), you can reconstruct a signal perfectly as long as you sample it at more than twice its highest frequency. Sample any slower and aliasing sets in: the excess folds back into the audible band as spurious tones. That's the reason ADCs put anti-aliasing filters ahead of the sampler.

Applications: ADC/DAC and hi-res audio

Settling on a sample rate means weighing bandwidth against file size. 44.1/48 kHz already covers the whole audible range; 96/192 kHz buys you headroom for non-linear processing and time-stretching, but it doubles or quadruples what lands on disk. Engineers reach for this when designing anti-aliasing filters, when arguing the 96/192 vs 44.1/48 hi-res question, and when planning oversampling in plugins that add distortion like saturation or clipping.

FAQ

Is 96 kHz audibly better than 44.1 kHz? It's a contested point. Blind tests suggest most listeners can't pick the difference on playback, though the processing gains for pitch shifting and time stretching are genuine.

What happens above the Nyquist limit? You get aliasing. Frequencies fold back symmetrically and leave inharmonic artifacts behind, which is exactly why anti-aliasing filters cut them off before sampling.

Why is CD 44.1 kHz and not 48 kHz? It comes down to history. The 44.1 kHz figure matched the PCM adapters that stored digital audio on early video tape recorders.