The Nyquist frequency is half the sample rate of a sampled system and represents the highest frequency that can be captured and reproduced without aliasing. In digital audio, a recording made at 48 kHz has a Nyquist frequency of 24 kHz, and any signal content above that limit must be removed before sampling.
The concept follows from the Nyquist-Shannon sampling theorem, which states that a band-limited signal can be reconstructed exactly from its samples if it contains no frequencies at or above half the sampling rate. The Nyquist frequency is a property of the system, not of the signal, and it should not be confused with the Nyquist rate, which is twice the highest frequency present in a given signal.
Why sampling has a frequency limit
Sampling measures a continuous signal at regular time intervals. To identify a sine wave unambiguously, the system needs more than two samples per cycle. At exactly two samples per cycle, the result depends on the phase: the samples may hit the peaks or land on the zero crossings and miss the wave entirely.
When a frequency above the Nyquist limit is sampled, its samples are identical to those of a lower frequency. The system cannot tell the two apart, so the high frequency appears in the recording as a false tone. This effect is called aliasing, and the false frequency is the alias.
The alias appears mirrored around the Nyquist frequency. For a sample rate of 48 kHz, a 30 kHz tone folds down to 18 kHz, which is well inside the audible range. Because the alias is usually not harmonically related to the original sound, it is heard as an inharmonic, unpleasant artifact that cannot be removed afterward.
Nyquist frequencies of common sample rates
The Nyquist frequency follows directly from the sample rate of the audio format. The table lists the standard rates used in audio production and delivery.
| Sample rate | Nyquist frequency | Typical use |
|---|---|---|
| 8 kHz | 4 kHz | Narrowband telephony |
| 16 kHz | 8 kHz | Wideband voice and speech recognition |
| 44.1 kHz | 22.05 kHz | Audio CD and music distribution |
| 48 kHz | 24 kHz | Video, broadcast and most production |
| 96 kHz | 48 kHz | High-resolution recording and processing |
| 192 kHz | 96 kHz | Specialized recording and measurement |
Human hearing extends at most to about 20 kHz in young listeners and declines with age. A Nyquist frequency of 22.05 or 24 kHz therefore leaves a narrow transition band between the top of hearing and the theoretical limit.
Anti-aliasing and reconstruction filters
Real converters cannot rely on the theorem alone, because real signals are rarely band-limited. An anti-aliasing filter before the analog-to-digital converter removes content above the Nyquist frequency, and a reconstruction filter after the digital-to-analog converter removes the spectral images created by playback.
Modern converters use oversampling: they sample internally at many times the target rate, use a gentle analog filter and then apply a steep digital decimation filter that does most of the work. This approach moves the difficult filtering into the digital domain, where it is precise and repeatable.
| Filter choice | Advantage | Trade-off |
|---|---|---|
| Steep linear-phase filter | Flat response up to about 20 kHz | Pre-ringing around transients |
| Minimum-phase filter | No pre-ringing | Phase shift near the top of the band |
| Gentle slow roll-off filter | Short impulse response | Some aliasing or images allowed through |
| Higher sample rate | Wider transition band, easier filtering | Larger files and more processing load |
The audible significance of these differences is debated. Controlled listening tests generally find small or no differences at 44.1 kHz and above with well-designed filters, while poor filter design can produce measurable artifacts in the top octave.
How the Nyquist frequency relates to other digital audio terms
The Nyquist frequency defines the frequency limit of digital audio, while other parameters define dynamic range and timing. The table separates these related concepts.
| Term | What it defines | Relation to the Nyquist frequency |
|---|---|---|
| Sample rate | Samples per second | Nyquist frequency is half of it |
| Bit depth | Resolution of each sample | Independent; sets dynamic range |
| Quantization | Rounding of sample values | Independent; adds noise across the band |
| Dither | Noise that linearizes quantization | Can be shaped toward the Nyquist region |
| PCM | Encoding of sample values | Bandwidth limited by the Nyquist frequency |
Noise-shaped dither is a practical example of the link: it moves quantization noise toward frequencies close to the Nyquist limit, where hearing is least sensitive, which improves perceived dynamic range at a given bit depth.
Aliasing inside audio processing
Aliasing is not only a converter problem. Nonlinear digital processing, such as distortion, saturation, clipping or aggressive compression, creates new harmonics. When those harmonics exceed the Nyquist frequency, they fold back as aliases inside the recording.
- Oversampling in plug-ins: many saturation and limiter plug-ins process internally at 2 to 16 times the session rate to keep harmonics below the internal Nyquist limit.
- Sample rate conversion: downsampling requires a new low-pass filter at the lower Nyquist frequency, or aliases appear.
- Synthesized waveforms: naive digital square and sawtooth waves alias heavily; band-limited oscillators avoid this.
- Inter-sample peaks: the reconstructed waveform can exceed 0 dBFS between samples, which true-peak meters detect.
Put simply
Digital audio works by taking snapshots of a sound many thousands of times per second. The Nyquist frequency is the highest pitch those snapshots can capture correctly. It is always exactly half the number of snapshots taken per second.
Sounds above that limit do not simply disappear. They come back disguised as false lower tones, much like a spinning wheel in a film that seems to turn backward. That is why recorders filter out such high sounds before taking the snapshots.
In practice
A sound designer records metal impacts and cymbal hits for a game. These sounds contain energy well above 20 kHz. The recorder runs at 96 kHz, giving a Nyquist frequency of 48 kHz and plenty of room for its anti-aliasing filter. The recordings will later be pitched down by two octaves, so the ultrasonic content becomes audible and useful.
For the final game build, the sounds are converted to 48 kHz. The conversion software applies a low-pass filter just below 24 kHz before downsampling. Without that filter, the ultrasonic energy would fold into the audible range as harsh, inharmonic tones. With it, the delivered files keep clean high frequencies without aliasing artifacts.