Nyquist–Shannon Sampling Theorem
Definición
A fundamental principle in digital audio stating that a digital audio signal must be sampled at a frequency at least twice the highest frequency present in the audio being recorded in order to accurately reconstruct that audio without loss of information. This minimum sampling rate is called the Nyquist frequency. For example, because human hearing extends to roughly 20 kHz, a sampling rate of 44.1 kHz (used for CDs) is sufficient because 44.1 kHz is more than twice 20 kHz. Without sampling at the Nyquist rate or above, aliasing occurs — high frequencies fold back into the audible spectrum and create unwanted artifacts.
En palabras simples
Sample faster than twice the highest frequency you want to capture, or you'll lose information and get weird artifacts. That's why CDs use 44.1 kHz (to capture up to 22 kHz) and professional recording uses 48 kHz (to capture up to 24 kHz). It's a hard limit, not a suggestion.
En la práctica
Audio containing frequencies up to 20 kHz requires a minimum sampling rate of 40 kHz to reconstruct without aliasing. CD audio at 44.1 kHz captures up to 22.05 kHz cleanly. If you try to record 48 kHz audio at only 44.1 kHz, frequencies above 22.05 kHz will alias back down into the audible range as noise.
Confusión común
The Nyquist theorem is often misunderstood as a ceiling ("sample at 44.1 kHz and everything above that disappears"), when it's really a floor ("sample below the Nyquist rate and aliasing ruins your recording"). Aliasing is not subtle phase issues — it's audible distortion and noise that cannot be removed in post-production. The solution is to low-pass filter (anti-aliasing filter) before sampling, or use a high enough sample rate that no audible content exists above the Nyquist frequency.
Fuentes y verificación
- Nyquist, H. — Certain topics in telegraph transmission theoryProceedings of the American Institute of Electrical Engineers, 1928
- Shannon, C. E. — Communication in the presence of noiseProceedings of the IRE, 1949
- Pohlmann, K. C. — Principles of Digital Audio (6th ed., sampling theorem chapter)McGraw-Hill, 2011
Última verificación: 2026-08-05