Digital Audio
The Nyquist theorem, or Nyquist–Shannon sampling theorem, defines the relationship between analogue and digital signals. It states that to reproduce a signal accurately, the sample rate must be at least twice the highest frequency contained in that signal.
The Nyquist theorem is a cornerstone of digital audio theory. It establishes the minimum sampling rate required to capture an analogue waveform without losing information. According to the theorem, if a signal contains frequencies up to a maximum of f hertz, it must be sampled at a rate of at least 2f hertz to be reconstructed correctly during playback.
In audio, this means that to reproduce frequencies up to 20 kHz — the upper limit of human hearing — a sample rate of at least 40 kHz is required. This principle directly influenced the design of digital audio systems such as the Compact Disc, which adopted a 44.1 kHz sampling rate to ensure a margin beyond the audible range.
When the Nyquist condition is not met, higher frequencies fold back into the audible spectrum, creating false tones known as aliasing. To prevent this, anti-aliasing filters are used before sampling to remove frequencies above half the sample rate — a limit known as the Nyquist frequency.
The theorem was first described mathematically by Harry Nyquist in 1928 and later formalised by Claude Shannon in 1949, becoming a foundation for all digital signal processing. In practice, every digital audio system — from early PCM recorders to modern DAWs — operates according to the Nyquist theorem.
