Calibration and uncertainty

A level printed by software is not yet a measurement. Two things separate the one from the other: knowing what the digital samples mean physically, and knowing how much the result could reasonably be wrong. This section covers both, and they apply transversally to every other page of the documentation.

Calibration and dBFS handles the first. phonometry works in two reference frames: physical dB SPL, established either from a recorded calibrator tone (the IEC 60942 field ritual) or from a known microphone sensitivity, and digital dBFS, levels relative to full scale, appropriate when no physical reference exists or when characterising the digital chain itself. The page explains how each mode is set up and, just as important, which quantities are meaningful in which frame.

Measurement uncertainty (GUM and Monte Carlo) handles the second, implementing the Guide to the Expression of Uncertainty in Measurement (ISO/IEC Guide 98-3:2008) and its Monte Carlo Supplement 1. The GUM route propagates standard uncertainties analytically through sensitivity coefficients into a combined and expanded uncertainty, with Welch-Satterthwaite effective degrees of freedom; the Monte Carlo route propagates whole probability distributions numerically and yields coverage intervals that stay honest when the model is non-linear or the inputs are far from Gaussian. The page shows both on the same models, including where they diverge and why.

Data qualification guards the gate in front of both: every average - a Leq, a Welch PSD, an uncertainty budget - assumes the record is stationary, and the Bendat & Piersol reverse arrangement and runs tests decide that objectively from segment mean squares, with the book’s own acceptance regions. The same page carries the Rice statistics of level crossings and peaks - apparent frequency, peak rates, the irregularity factor - that characterize a qualified Gaussian record and screen for one that is not.

The same discipline extends into the frequency domain: the Signals and spectra pages apply the Bendat & Piersol error analysis to Welch spectral estimates, so every PSD carries its effective number of averages, its normalized random error and a chi-square confidence interval.

The pages meet in practice: an uncertainty budget for an acoustic measurement almost always contains a calibration term, and several standards implemented elsewhere in the library (ISO 9612, ISO 12999-1) ship uncertainty budgets that are specialisations of the GUM machinery described here.

Pages in this section

• Calibration and dBFS: physical SPL calibration from a calibrator tone or a known sensitivity, and the digital full-scale mode.
• Measurement uncertainty (GUM and Monte Carlo): the law of propagation of uncertainty and the Monte Carlo method, expanded uncertainty and coverage intervals.
• Data qualification: the reverse arrangement and runs stationarity tests on segment statistics, and the Rice level-crossing and peak statistics with the irregularity factor.