ETM Learn · 07 / 08

Limiting: peaks and the cost of reducing them

Separate clipping, moving gain, sample peaks, reconstructed peaks and loudness.

01 · Understand

After compression, examine control of peaks relative to a ceiling. A limiter usually moves gain over time. A clipper instead limits amplitude values themselves. Both can alter sound, so listen for the cost as well as watching the meter.

Digital audio is a sequence of samples, values at separate instants. Sample peak is their largest absolute value. The reconstructed wave may peak between samples; estimates that maximum. Start with the correct limiter mode and raise Drive gradually. Then explore Lookahead, which delays audio relative to detection.

Terms within reach

Dotted terms offer a definition on hover, keyboard focus or tap. Click to keep it open; Escape or an outside click closes it. All definitions are also available here.

True peak

An estimate of the reconstructed waveform's peak, including between samples. Accuracy depends on reconstruction; this teaching meter is not certified.

Crest factor

Peak-to-RMS ratio over the same measurement interval. Describes the peak relative to effective level, not perceived loudness alone.

LUFS

Loudness units relative to full scale using weighting and time aggregation. Specify whether the measurement is momentary, short-term or integrated.

02 · Play & discover

Select limiter and the correct kernel. Raise drive gradually and compare waveform, gain reduction and spectrum.

Predict → change one control → compare → explain the result.

Experiment 01

Intentionally faulty modes violate conditions in this implementation. They do not describe every limiter. Reconstructed peak and loudness readings are estimates.

Limiter Bench

idle
The loop - dry vs limited, with the ceiling
Gain reduction · 48 kHz analysis model
Transfer curve - measured
Spectrum - dry vs limited
dry limited gain reduction ceiling true-peak overshoot
vol
audio starts on first click
Max GR-
Sample peak-
True peak estimate-
Over ceiling-
Mono LUFS estimate-
Crest factor-

Experiment 02

More lookahead permits attenuation before the delayed peak, but affects a longer neighbourhood and costs latency. This is pre-attenuation, not filter pre-ringing.

The gain envelope around a single peak

-
no smoothing (running minimum) boxcar - exactly triangular cascaded boxcar - C¹ smooth the peak
Pre-duck starts-
Total disturbance-
Latency it costs-

Experiment 03

Set 0.25 × fs and 45°. The reconstructed sine can exceed its largest sample. This is ideal sine reconstruction; actual filters and lossy coding can change the result.

Inter-sample peaks - what the converter actually plays

-
the samples stored the waveform reconstructed between them 0 dBFS
Sample peak-
True peak estimate-
Hidden overshoot-

Check your understanding

Does sample peak below 0 dBFS guarantee reconstructed peak below it?

03 · Go deeper

A nonnegative normalized smoothing kernel confined to a suitable window can preserve the ceiling in this running-minimum design. These are sufficient conditions here, not necessary conditions for every limiter. IIR smoothing is not inherently oscillatory, but smoothing without a suitable safety constraint can miss peaks.

The peak meter uses finite 8× windowed-sinc interpolation with periodic extension. It is not a certified BS.1770 meter: finite filtering and time resolution limit accuracy. Loudness uses mono K-weighting and gated 400 ms blocks; loop length and startup affect it. This is not a full stereo programme measurement.

is 20 log₁₀(peak/RMS), with consistent peak definition and interval. PLR is dBTP minus integrated , a different metric. Normalization depends on service, mode and device. No universal streaming target or ceiling exists; check the current delivery specification and listen to the processing.

The mathematics in words

Peak-to-RMS ratio

CF = 20 log₁₀(peak / RMS)

Divide peak amplitude by RMS of the same interval and convert to dB. A steady sine has ratio √2, about 3.01 dB. For total silence the ratio is undefined.

Peak-to-loudness ratio

PLR = peak[dBTP] − loudness[LUFS integrated]

Subtract integrated LUFS from peak dBTP. Example: peak −1 and loudness −13 give 12 dB. This differs from crest factor because LUFS is not plain RMS.

Numerical challenge: try before revealing the solution

01 · An ideal sine at fs/4 and phase 45° is scaled until its sample peak is 1. How far above 0 dBFS is its reconstructed peak?

Hint

Before scaling, the largest sample is 1/√2 of the sine amplitude.

Solution & assumptions

Scaling is √2, so the reconstructed peak is √2 and 20 log₁₀(√2) = 3.0103 dB. This is an ideal band-limited sine calculation, not a universal inter-sample overshoot bound for music.

02 · For one measurement interval, peak is −1 dBFS and RMS referenced to amplitude 1 is −13 dBFS. What is crest factor?

Hint

Subtract RMS level from peak level, using consistent amplitude references.

Solution & assumptions

−1 − (−13) = 12 dB, corresponding to peak/RMS = 10^(12/20) ≈ 3.981. Replacing RMS with integrated LUFS produces a different quantity, PLR, and cannot be justified by changing the label alone.

Further reading: ITU-R BS.1770