Definition
Clipping is the limiting of a signal's amplitude to a maximum value c: the part of the waveform beyond the threshold is cut off or rounded.
- Hard clipping: y = sgn(x) · min(|x|, c). The waveform becomes flat above the threshold and the transfer function has a corner.
- Soft clipping: a continuous function with a continuous derivative, which approaches the limit gradually. Examples: y = tanh(k·x) / tanh(k); the cubic polynomial y = 1.5·x − 0.5·x³ for |x| ≤ 1 and y = ±1 beyond.
Digital clipping: in fixed point, every value beyond full scale is replaced with the maximum representable value; it is hard clipping. The harmonics generated above the Nyquist frequency (fs/2) do not disappear: they fold back into the audible band at the frequencies |k·fs − n·f0| (aliasing) and are not harmonically related to the note. Analog clipping: transistor and op-amp stages clip sharply near the supply voltage; tubes, transformers and tape clip gradually. Analog clipping does not produce aliasing, but the signal must then be converted without exceeding full scale.
A symmetric (odd) transfer function generates only odd harmonics (3rd, 5th, 7th…); an asymmetric one also generates even harmonics and a DC component. In the limit, very deep clipping turns the sine wave into a square wave, with odd harmonics of amplitude 1/n.
Parameters and units
- Threshold or ceiling: dBFS or, in processors, dB relative to the input level.
- Drive / input gain: how much signal is pushed beyond the threshold (dB).
- Softness / knee: width of the transition zone between linear behavior and limiting.
- Oversampling: ×2–×16; reduces aliasing by processing at a higher sample rate.
- Symmetry / bias: introduces even harmonics.
- Measurements: THD (%), number of consecutive samples at full scale, crest factor reduction.
Harmonic distortion of a sine wave subjected to hard clipping:
| Clipping below the peak | THD | 3rd harmonic |
|---|---|---|
| 0.9 dB | 4.2% | −29.7 dB |
| 3.0 dB | 13.4% | −17.7 dB |
| 6.0 dB | 23.3% | −12.9 dB |
Musical function
Unintentional clipping is a defect: it produces harsh distortion, crackling and, in digital, inharmonic components from aliasing. Intentional clipping is a tool: a clipper on the drum bus or before the mastering limiter cuts very brief peaks by 1–3 dB with no attack or release times, and therefore without pumping, and raises loudness at the same peak level. On transients lasting a few milliseconds, the distortion introduced is masked by the transient itself. Soft clipping is also a form of saturation, used to give density to basses, 808s and drums.
Practical example
- Aliasing: 3 kHz sine wave with hard clipping at 44.1 kHz. The odd harmonics at 9, 15 and 21 kHz remain in band; those at 27, 33 and 39 kHz fold back to 17.1, 11.1 and 5.1 kHz, frequencies foreign to the note. With ×8 oversampling the harmonics above 22 kHz are filtered out before returning to 44.1 kHz.
- Clipper on the drum bus: the snare has peaks 4 dB above the body of the sound. A clipper with 2 dB of clipping and ×4 oversampling brings the bus crest factor from 14 to 12 dB; at the same peak level the bus loudness rises by 1.5 LU and the transient remains perceptible.
- Master: a soft clipper with 1–1.5 dB of reduction before a limiter that itself works for 1–2 dB spreads the work and reduces the artifacts of both.
Common mistakes
- Using clippers and saturators without oversampling on bright material: aliasing makes cymbals and vocals sound metallic.
- Leaving runs of 3 or more samples at full scale in the master.
- Assuming that a signal above 0 dBFS in a floating-point DAW is already clipping and, conversely, failing to notice that it becomes so in the 24-bit export or at the converter.
- Clipping the interface input: analog clipping cannot be recovered.
- Judging clipping at a low listening volume, where distortion is less perceptible.
- Stacking several clipping stages along the chain without checking the total.
How to check it
- App analysis: the Clipped sections (≥3 samples at full scale) row counts the points where at least 3 consecutive samples reach ±0.999 of full scale; the Inter-sample peaks above 0 dBFS row detects overshoots in the reconstructed waveform. The Crest factor (peak − RMS) drops when a clipper is working.
- Aliasing test: send a 3–5 kHz sine wave to the clipper and observe the spectrum: components below the note's frequency or between the harmonics indicate aliasing.
- Listening check: listen to the difference signal (input − output, with the polarity inverted on one of the two): it should contain only brief traces on the transients.
Starting settings
| Parameter | Value | Why |
|---|---|---|
| Clipper on the drum bus | 1–3 dB of reduction | Peak control without pumping. |
| Clipper in mastering | 0.5–1.5 dB, before the limiter | Spreads the work and reduces artifacts. |
| Oversampling | ×4–×8 | Reduces aliasing of the high harmonics. |
| Soft clipping on 808s and basses | drive 3–6 dB | Harmonics that make the bass audible on small speakers. |
| Clipping in the final file | 0 runs of ≥3 samples at full scale | Common acceptance criterion for masters. |
| Converter input | peaks ≤ −6 dBFS | Analog clipping during recording cannot be recovered. |
How to check the result
- Clipped sections (≥3 samples at full scale) = 0 in the master and in the recorded tracks.
- Inter-sample peaks above 0 dBFS = 0 in the master.
- The crest factor of the drum bus drops by no more than 3 dB because of the clipper.
- No inharmonic component visible in the spectrum with a 3–5 kHz test sine wave through the clipper.