Source: https://jmrplens.github.io/phonometry/guides/calibration/ # Calibration and dBFS Every level this library reports is only as trustworthy as the one number this page produces: the sensitivity factor that converts digital units into pascals. The page covers both reference frames a recording can be analyzed in: physical **dB SPL**, obtained by calibrating the chain against an IEC 60942 acoustic calibrator, and digital **dBFS**, levels relative to full scale with no physical claim attached. Choosing between them is a question about your measurement chain, not about preference. Work in dB SPL whenever the result faces a physical criterion (a noise limit, an exposure threshold, any acoustics standard); that requires a calibrator recording made through the *same, untouched* chain as the measurement. Work in dBFS when the signal never had a calibrated analog front end (loudness normalization, codec and interface tests, file-only analysis) or when no calibration tone exists, in which case absolute SPL statements are simply out of reach. The workflow around the factor matters as much as the formula: derive it before and re-check it after each session, verify meter and calibrator periodically in the laboratory (IEC 61672-3 and IEC 60942; Bies, Hansen & Howard 2017, §3.4), and treat the pre/post difference as your drift bound. The field, laboratory and drift section below turns that into concrete rules, and the [Build a sound level meter](https://jmrplens.github.io/phonometry/guides/sound-level-meter/) walkthrough starts from exactly this step before any level is computed. ## Why calibrate? The theory A digital recording only knows *numbers*: a full-scale sine wave is ±1.0 regardless of whether it was a whisper or a jet engine. To report physical sound pressure levels the chain microphone → preamplifier → ADC must be characterized by a single number, the **sensitivity factor** $S$, that converts digital units into pascals: $$ p(t) = S\ x(t) \qquad S = \frac{p_\text{ref}\cdot 10^{L_\text{cal}/20}}{\tilde{x}_\text{ref}} $$ where $L_\text{cal}$ is the calibrator's level (typically 94 dB, i.e. 1 Pa), $p_\text{ref} = 20\ \mu\text{Pa}$ and $\tilde{x}_\text{ref}$ is the RMS of the recorded calibration tone in digital units. `sensitivity()` is exactly that equation. The factor is valid as long as nothing in the chain changes: touch the gain knob and you must recalibrate. ## Physical Calibration (Sound Level Meter) To get accurate SPL measurements from a digital recording, you must first calculate the sensitivity of your measurement chain using a reference tone (e.g., 94 dB @ 1 kHz). ```mermaid flowchart LR A["Calibrator tone\n94 dB @ 1 kHz\n(IEC 60942)"] --> B["Recording\ncalibrator_recording"] B --> C["sensitivity()"] C --> D["calibration_factor\n(digital units → Pa)"] D --> E["octave_filter / leq / laeq / ln_levels"] F["Measurement\nrecording"] --> E E --> G["Levels in dB SPL\n(re 20 µPa)"] ``` ```python import numpy as np from phonometry import metrology # 1. Record your 94 dB calibrator signal (1 kHz, 1 Pa RMS = 94 dB SPL) fs = 48000 # calibrator_recording: your recorded 1 kHz calibrator tone (1 Pa RMS = 94 dB SPL). # Synthesized here so the guide runs; in a real measurement, record your calibrator. calibrator_recording = np.sqrt(2) * np.sin(2 * np.pi * 1000 * np.arange(fs) / fs) # recording: the mic capture you want to calibrate, same input chain (Pa after calibration). # Synthesized here; in a real measurement this is your recorded signal. recording = 0.2 * np.sin(2 * np.pi * 1000 * np.arange(fs) / fs) # 2. Calculate the sensitivity factor calibration_factor = metrology.sensitivity(calibrator_recording, target_spl=94.0, fs=fs) # 3. Apply calibration to your measurements spl, freq = metrology.octave_filter(recording, fs, calibration_factor=calibration_factor) # Now 'spl' values are in real-world dB SPL! ``` The same `calibration_factor` works across the whole library: `octave_filter`, `OctaveFilterBank`, `leq`, `laeq` and `ln_levels`. ## Calibrator assumptions (IEC 60942) `sensitivity` assumes the reference recording comes from an acoustic calibrator as specified by **IEC 60942** (classes LS, 1 and 2): - The default `target_spl=94.0` matches the common 94 dB @ 1 kHz calibrator output (the standard requires the principal level to be at least 90 dB re 20 µPa; 94 dB and 114 dB are the usual choices). - The resulting sensitivity inherits the calibrator's class tolerance (e.g. ±0.4 dB for a class 1 calibrator between 160 Hz and 1.25 kHz, IEC 60942 Table 1) plus the RMS estimation error of your recording. - IEC 60942 specifies the generated level as a 20 s average: record a few seconds of *stable* tone (excluding handling noise at the start/end) for the RMS estimate to converge. ### Automatic stability validation When you pass the sample rate (and `validate=True`, the default), `sensitivity(ref, fs=fs)` checks the recording the way IEC 60942:2017 checks the calibrator itself (5.3.3): the *short-term level fluctuation*, the absolute difference between each of the maximum and minimum F-time-weighted levels and the mean level, must not exceed the Table 2 class 1 limit for the calibrator's nominal frequency (0.07 dB at and above 160 Hz, relaxed to 0.10 dB below 160 Hz and 0.20 dB at or below 63 Hz, where the F time-weighting itself ripples). Pass `frequency=` to select the right row for non-1 kHz calibrators. A `CalibrationWarning` flags badly coupled microphones or handling noise before they silently corrupt every calibrated level. The recording must be at least 2 s long (1 s for the F-integrator to settle plus 1 s of settled envelope); shorter recordings get a warning instead of an unreliable verdict. Without `fs` the check is skipped. Override the limit with `max_fluctuation_db` or disable with `validate=False`. The check catches exactly what ruins field calibrations (a loose coupler, wind, handling noise):

Show the code for this figure

```python import matplotlib.pyplot as plt import numpy as np from phonometry import metrology fs = 48000 t = np.arange(int(fs * 6.0)) / fs stable = 0.5 * np.sin(2 * np.pi * 1000 * t) # 3 % amplitude modulation at 2 Hz: ~0.14 dB of wobble, clearly over unstable = stable * (1 + 0.03 * np.sin(2 * np.pi * 2.0 * t)) plt.figure(figsize=(9, 5)) skip = fs # discard the F-integrator attack (~8 tau) for x, label in ((stable, "Stable tone (good coupling)"), (unstable, "3% AM tone (loose coupling)")): env = metrology.time_weighting(x, fs, mode="fast")[skip:] level = 10 * np.log10(np.maximum(env, np.finfo(float).eps)) plt.plot(t[skip:], level - level.mean(), label=label) for lim in (0.07, -0.07): plt.axhline(lim, linestyle="--", color="gray") plt.xlabel("Time [s]") plt.ylabel("F-weighted level re mean [dB]") plt.legend() plt.show() ```

### `sensitivity()` parameters | Parameter | Type / shape | Units | Range / default | Notes | | :--- | :--- | :--- | :--- | :--- | | `ref_signal` | 1D/2D array | digital units | non-empty, non-silent | Recording of the calibration tone only (trim handling noise) | | `target_spl` | float | dB re 20 µPa | default `94.0` | The calibrator's nominal level (114 dB calibrators: pass `114.0`) | | `ref_pressure` | float | Pa | default `2e-5` | Reference pressure p₀; rarely changed | | `fs` | int, optional | Hz | > 0; default `None` | Required for the stability validation; omit to skip it | | `validate` | bool | — | default `True` | Emit `CalibrationWarning` on unstable/short recordings | | `max_fluctuation_db` | float, optional | dB | default `None` → Table 2 class 1 | Explicit override of the stability limit | | `frequency` | float | Hz | default `1000.0` | Calibrator's nominal frequency; selects the IEC 60942 Table 2 row | | `narrowband` | bool | — | default `False` | Estimate the tone with a coherent Goertzel detector near `frequency` (needs `fs`) instead of full-band RMS; rejects broadband hum/noise that otherwise inflates the RMS and shrinks every later level (~−0.44 dB at 20 dB SNR). Enable for noisy coupler recordings | Returns the sensitivity factor (float) to pass as `calibration_factor=` to `octave_filter`, `leq`, `laeq`, `ln_levels`, `lc_peak`, `sel` and the dose functions. ## Field checks, laboratory verification and drift Calibration lives at three time scales: - **Every session: the field check.** Couple the calibrator and derive the sensitivity before each measurement series, and check it again at the end. Normative methods make the second check mandatory and use the pre/post difference as a validity gate (a common criterion invalidates the series when the two differ by more than 0.5 dB). Whatever the threshold, the difference is your drift bound for everything captured in between; carry it into the uncertainty budget rather than assuming zero. - **Periodically: laboratory verification.** A field check only compares the chain against the calibrator; it cannot see an error the calibrator and meter share, and it says nothing about the response away from 1 kHz. IEC 61672-3 defines the periodic tests for the meter (weightings, level linearity and ballistics spot-checked against the class limits), and IEC 60942 the corresponding tests for the calibrator itself; typical laboratory intervals are one to two years. - **Between checks: drift.** Microphone sensitivity moves with temperature, humidity and capsule aging; electronics with battery voltage. A healthy class 1 chain drifts a few hundredths of a dB over a session, which is why a pre/post difference of half a decibel signals damage rather than weather. The largest "drift" of all is a touched gain knob: the factor S is valid only while the chain stays exactly as calibrated. One more class subtlety: tolerances chain. A class 1 measurement requires a class 1 (or LS) calibrator *and* a class 1 meter; calibrating a class 1 chain with a class 2 calibrator silently downgrades every derived level to class 2 accuracy, because the calibrator's wider level tolerance enters S directly. ## Digital Analysis (dBFS) If you are working with digital audio files (e.g., WAV, FLAC) and want to analyze levels relative to Full Scale rather than physical pressure, you can use the `dbfs=True` parameter. In this mode: * **0 dBFS** corresponds to a numeric signal level of 1.0 (RMS or Peak). * `calibration_factor` does not apply (dBFS is relative to digital full scale). * Useful for analyzing headroom, digital mastering, or normalized signals. ```python import numpy as np from phonometry import metrology fs = 48000 # recording: the mic capture you want to calibrate, same input chain (Pa after calibration). # Synthesized here; in a real measurement this is your recorded signal. recording = 0.2 * np.sin(2 * np.pi * 1000 * np.arange(fs) / fs) # Assume 'recording' is normalized between -1.0 and 1.0 spl_dbfs, freq = metrology.octave_filter(recording, fs, dbfs=True) # Results will be negative (e.g., -20 dBFS) ``` ## RMS vs Peak Levels phonometry supports two measurement modes to align with professional software like BK: - **RMS (`mode='rms'`)**: Energy-based level (standard). - **Peak (`mode='peak'`)**: Absolute maximum value reached in the frame (Peak-holding). ```python import numpy as np from phonometry import metrology fs = 48000 # recording: the mic capture you want to calibrate, same input chain (Pa after calibration). # Synthesized here; in a real measurement this is your recorded signal. recording = 0.2 * np.sin(2 * np.pi * 1000 * np.arange(fs) / fs) # Measure peak-holding levels for impact analysis spl_peak, freq = metrology.octave_filter(recording, fs, mode='peak') ``` > [!NOTE] > `mode='peak'` measures the absolute maximum of the **filtered** band signal, > which includes the filter's onset transient (overshoot). Signals that start > abruptly may read up to ~1 dB high. This is inherent to IIR band filters > (an analog SLM behaves the same way), not a processing artifact. ## Integer audio input Integer signals (e.g. int16 from `scipy.io.wavfile.read`) are converted to float64 internally before any squaring, so calibration and level results are identical whether you pass the raw integer array or a float conversion. ## Quick answers ### What calibrator level should I use to calibrate my measurement chain? The usual choice is 94 dB SPL at 1 kHz (1 Pa RMS), which is what `sensitivity()` assumes with its default `target_spl=94.0`; for a 114 dB calibrator pass `114.0`. IEC 60942 requires the principal level to be at least 90 dB re 20 µPa. Record a few seconds of stable tone, because the standard specifies the generated level as a 20 s average. ### How much drift between the pre and post calibration checks is acceptable? Derive the sensitivity before each measurement series and check it again at the end: a common criterion invalidates the series when the two differ by more than 0.5 dB. A healthy class 1 chain drifts a few hundredths of a dB over a session, so a half-decibel pre/post difference signals damage rather than weather. Whatever the threshold, carry the difference into the uncertainty budget rather than assuming zero. ### Can I calibrate a class 1 chain with a class 2 calibrator? You can, but the tolerances chain: a class 1 measurement requires a class 1 (or LS) calibrator per IEC 60942 and a class 1 meter, so a class 2 calibrator silently downgrades every derived level to class 2 accuracy, because its wider level tolerance enters the sensitivity factor $S$ directly. For reference, the class 1 tolerance is ±0.4 dB between 160 Hz and 1.25 kHz (IEC 60942 Table 1). ## References - International Electrotechnical Commission. (2017). *Electroacoustics — Sound calibrators* (IEC 60942:2017). [IEC webstore](https://webstore.iec.ch/en/publication/30045). The calibrator classes, level tolerances and the short-term stability criterion `sensitivity()` applies to the reference recording. - International Electrotechnical Commission. (2013). *Electroacoustics — Sound level meters — Part 3: Periodic tests* (IEC 61672-3:2013). [IEC webstore](https://webstore.iec.ch/en/publication/5710). The laboratory verification procedure behind the periodic checks recommended above. - Bies, D. A., Hansen, C. H., & Howard, C. Q. (2017). *Engineering noise control* (5th ed.). CRC Press. [doi:10.1201/9781351228152](https://doi.org/10.1201/9781351228152). Sections 3.1.5 and 3.4 (microphone field effects and sound level meter calibration: the electrical and acoustic calibration practice this page's workflow follows). ISBN 978-1-4987-2405-0. ## Standards IEC 60942:2017, *Electroacoustics — Sound calibrators* — the calibrator level and class assumptions behind `sensitivity()` (the 94 dB principal level and the Table 1 class tolerances) and the short-term level-fluctuation stability check of the reference recording (5.3.3, Table 2 class 1 limits per nominal frequency).