Inter-sample peak

Definition

An inter-sample peak is a value of the reconstructed waveform that exceeds, in absolute value, the samples surrounding it. The analog signal that the D/A converter produces is, ideally, the interpolation of the samples with the sinc function:

x(t) = Σ x[n] · sinc((t − n·T) / T), with T = 1/fs.

This curve passes through all the samples but between one sample and the next it can rise above them. We speak of an inter-sample over when the reconstructed peak exceeds 0 dBFS even though no sample does: the file is formally valid, but the converter, the resampler or the lossy decoder working in fixed point produces clipping.

Reference example: a sine wave at fs/4 with a phase of 45° has samples at ±sin(45°) = ±0.707 of the amplitude. If the file is normalized so that the samples equal 0 dBFS, the reconstructed peak is +3.01 dBTP. For deliberately constructed sample sequences the excess can be even greater. Inter-sample overs arise mainly from limiters and clippers without oversampling (which produce consecutive samples at the same amplitude), from normalization to 0 dBFS and from material very rich in high frequencies.

Parameters and units

• Unit: dBTP for the reconstructed value; count of excursions above 0 dBFS.
• Measurement method: ×4 oversampling with an interpolation filter (ITU-R BS.1770-4); maximum underestimate 0.69 dB.
• Typical excess of true peak over sample peak: 0–0.5 dB on unlimited mixes; 0.5–1.5 dB on limited masters without oversampling; up to 3 dB on clipped, bright material.
• Safety margin: true peak ≤ −1 dBTP.

Musical function

The inter-sample peak determines whether the master stays clean in every stage of playback. Many consumer converters and some reconstruction filters have no margin above 0 dBFS and clip the overs; AAC and MP3 decoders add their own overshoots to those already present. The result is brief, harsh distortion on the loudest hits, audible especially on cymbals, sibilant vocals and bright synths.

Practical example

• Test signal: sine wave at 11,025 Hz (fs/4 at 44.1 kHz), phase 45°, samples normalized to 0 dBFS. The sample-peak meter reads 0.0 dBFS, the true-peak meter reads +3.0 dBTP.
• Real master: limiter in sample-peak mode with a ceiling of −0.1 dBFS. The analysis shows a sample peak of −0.1 dBFS, a true peak of +0.8 dBTP and 340 inter-sample peaks above 0 dBFS. With the limiter in true-peak mode, ceiling −1.0 dBTP and ×4 oversampling, the count drops to 0 and the integrated loudness falls by 0.3 LU.

Common mistakes

• Assuming that a sample peak of −0.1 dBFS rules out clipping on playback.
• Using clippers and limiters without oversampling and without true-peak mode on the master.
• Normalizing the master to 0 dBFS after the limiter.
• Considering inter-sample overs inaudible in every case: it depends on the converter and the codec, so the master must be corrected regardless.
• Leaving a margin of 0.1–0.3 dB for files destined for lossy encoding.

How to check it

• App analysis: the Inter-sample peaks above 0 dBFS row counts the values interpolated with ×4 oversampling that exceed full scale; the True peak (×4, BS.1770) row reports their maximum. The value must be 0 in the master.
• Comparison: the difference between True peak and Sample peak shows how much the master generates inter-sample peaks.
• Dedicated meters: Youlean Loudness Meter, FabFilter Pro-L 2, iZotope Insight with dBTP readout.
• Decoder test: encode the master to AAC or MP3, decode it and remeasure the true peak.