Peak (sample peak)

Definition

The sample peak is the maximum absolute value reached by the samples of a digital signal over a time interval:

P = max |x[n]|

It is expressed in dBFS (decibels relative to full scale): L_peak = 20 · log10(P / FS), where FS is the full-scale value (1.0 in normalized floating point, 2^(N−1) − 1 in N-bit integers; 32767 at 16 bits). In fixed point, 0 dBFS is the largest representable sample and any value beyond it is truncated (clipping). In 32-bit floating point, samples can exceed 1.0, that is, take positive dBFS values, without any loss of information as long as the signal stays inside the DAW engine; the limit becomes rigid again at conversion to fixed point, at the D/A converter and in all plugins that model circuits with a saturation threshold.

The sample peak only describes the values of the samples, not the reconstructed waveform: between two samples the analog signal can exceed both values (inter-sample peak, see the dedicated guide). For this reason the sample peak is always less than or equal to the true peak. A digital peak meter has zero integration time (every sample counts), a bar fall-back time on the order of 10–20 dB/s and a maximum indicator (peak hold). The analog PPM (Peak Programme Meter), on the other hand, integrates over 5 or 10 ms and does not read shorter peaks.

Parameters and units

• Unit: dBFS. In fixed point the values are always ≤ 0 dBFS.
• Useful relationships: half the amplitude = −6.02 dB; amplitude 0.891 = −1.0 dBFS; amplitude 0.708 = −3.0 dBFS; amplitude 0.5 = −6.02 dBFS; 16384 at 16 bits = −6.02 dBFS.
• Peak hold: time for which the indicator stays on the maximum value (2–3 s while working, infinite when checking).
• Over: many meters flag clipping when they find at least 3 consecutive samples at full scale; a single sample at 0 dBFS is not counted.
• Channels: the peak is read per channel; the peak of a stereo file is the maximum between the two channels.
• Related quantities: true peak (dBTP), RMS, crest factor (peak − RMS), PLR (true peak − integrated loudness).

Musical function

The sample peak shows how much margin remains before the digital limit. It is used in gain staging (recording level, track and bus levels), in checking files for delivery and in diagnosing clipping. It does not indicate perceived loudness: two masters with the same peak of −0.3 dBFS can differ by 8–10 LU in loudness, because loudness depends on average energy and spectrum, not on the maximum instantaneous value. In the mix, the peak is a technical constraint; level decisions between instruments are made by listening and by measuring loudness.

Practical example

Reference values for a 24-bit floating-point production:

Reading example: a kick with a peak of −4.2 dBFS on its single track has a margin of 4.2 dB; summed with the bass, which has a peak of −6.0 dBFS, it can produce peaks on the bus of up to 20 · log10(10^(−4.2/20) + 10^(−6/20)) = +1.0 dBFS if the two peaks coincide in phase. Lowering both tracks by 8 dB brings the bus to −7 dBFS in the worst case and restores the margin.

Common mistakes

• Using the peak as a measure of volume: normalizing two songs to a 0 dBFS peak does not make them equally loud.
• Considering a master with a sample peak of −0.1 dBFS safe: the true peak may be above 0 dBTP and lossy encoding adds further peaks.
• Treating a value above 0 dBFS on an internal track of a floating-point DAW as clipping, while overlooking plugins that model analog gear, which already saturate at lower levels.
• Reading the post-fader meter and missing that an insert plugin before the fader is saturating.
• Using a VU or RMS meter to check peaks: they integrate over hundreds of milliseconds and read 8–15 dB below the real peak.
• Normalizing the master on the peak as a last step, after dither: normalization changes the level and cancels the effect of the dither calculated beforehand.

How to check it

• DAW meters: in FL Studio the mixer meters show the peak per channel; Wave Candy in Peak meter mode shows the numeric value.
• App analysis: the Sample peak row of the analysis panel is the maximum absolute value over both channels of the file, in dBFS. The Clipping sections (≥3 samples at full scale) row counts the points where at least 3 consecutive samples exceed ±0.999 of full scale.
• Comparison with the true peak: the app also reports True peak (×4, BS.1770); the difference between true peak and sample peak is 0–0.5 dB in lightly limited material and reaches 1–3 dB in saturated, very bright masters.
• Practical test: export the mix as a 24-bit WAV, analyze it in the app and check that the peak is in the expected range for the work phase.