Calibration and uncertainty

A level printed by software is not yet a measurement. Three things separate the one from the other: knowing that the record deserves to be averaged at all, knowing what the digital samples mean physically, and knowing how much the result could reasonably be wrong. This section covers all three, and they apply transversally to every other page of the documentation. A fourth page maps the evidence that backs the numbers: what a performance class asserts, the verifiers that grade a chain, and the published conformance report.

Calibration and dBFS handles the physical meaning. phonometry works in two reference frames: physical dB SPL, established from a recorded calibrator tone (the IEC 60942 field ritual), 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, and it grades the calibrator itself against IEC 60942:2017 from what a laboratory measured on it.

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.

Compliance and verification carries the evidence story: what a performance class actually claims in IEC 61672-1 and IEC 61260-1 (same design goals, different acceptance limits), which public verifier grades each stage of a measurement chain against its tolerance tables, the conformance rule of IEC TC 29 that grades a measured instrument, how to read and cite the numerical conformance report the site publishes, and the honest boundary against the pattern-evaluation and periodic tests of IEC 61672-2/-3 and IEC 61260-2/-3: the measurements need an instrument in a laboratory rather than a library, and what the library does with them is grade the results (filters.verify_filter_periodic for the periodic tests of a band filter) and compute on a design the tests that need no specimen.

Data qualification guards the gate in front of both: every average - a Leq, a Welch PSD, every averaged input to 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 characterise a qualified Gaussian record and screen for one that is not.

Random-incidence and diffuse-field response takes the calibration of the meter itself beyond its reference direction: the IEC 61183 directivity factor from readings in an anechoic room, the random-incidence sensitivity level that follows from it, and the diffuse-field level by comparison with a reference meter in a reverberation room.

Free-field corrections bring a meter tested on a sound calibrator, a comparison coupler or an electrostatic actuator back to the free field it is specified for: the IEC 62585 adjustment value at the calibration check frequency, the correction at each frequency, the uncertainty budget that goes with it, and the maximum each clause permits.

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.

• Calibration and dBFS: physical SPL calibration from a calibrator tone, the stability check it applies to that recording, the IEC 60942:2017 verdict on the calibrator itself, and the digital full-scale mode.
• Compliance and verification: what a performance class asserts, the verifiers that grade weightings, filter banks and intensity spectra against their tolerance tables, the conformance rule of IEC TC 29, the conformance report, and the scope of IEC 61672-2/-3 and IEC 61260-2/-3.
• 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.
• Random-Incidence and Diffuse-Field Response (IEC 61183): the directivity factor of a sound level meter from readings in two planes, one plane or 38 equal-area elements, its random-incidence and diffuse-field sensitivity levels, and Table B.1 of the reference microphone.
• Free-Field Corrections of a Sound Level Meter (IEC 62585): the adjustment value, the corrections for a calibrator, a coupler and an actuator, the budget of Annex I and the verdict of clauses 9 to 14.

• Nothing here measures an instrument or a calibrator. No IEC 60942 test is performed: verify_sound_calibrator grades the numbers a laboratory measured on a calibrator, and the static-pressure correction of an LS/M or 1/M pistonphone comes from its manual, so pass an already corrected target_spl when the manual asks for one; the IEC 61672-3 periodic tests are cited as laboratory practice rather than run; Compliance and verification draws that boundary precisely, part by part. The dBFS half of the calibration page sits outside any standard and makes no physical claim: it is a reference frame, not a measurement. Data qualification implements the quantitative core of Bendat & Piersol’s section 10.3 only: classifying a record’s type, validating it against physical limits and editing out glitches remain manual steps, as the book describes them. And an uncertainty budget is a model of your measurement: the library propagates whatever you declare, and never invents the terms. Where a standard publishes its own budget the guides say so, as ISO 9612 does for occupational exposure and ISO 12999-1 for sound insulation.