---
title: "API Reference"
description: "Every public function and class in phonometry."
---

All core functionality can be imported directly from the `phonometry` package.

| Name | Type | Description (Inputs) | Usage Snippet (Outputs) |
| :--- | :--- | :--- | :--- |
| `octave_filter` | `function` | **High-level analysis.**<br>• `x`: Signal array<br>• `fs`: Sample rate [Hz]<br>• `fraction`: 1, 3, etc. (Default: 1)<br>• `order`: Filter order (Default: 6)<br>• `limits`: [f_min, f_max] (Default: [12, 20000])<br>• `filter_type`: 'butter', 'cheby1', 'cheby2', 'ellip', 'bessel' (Default: 'butter')<br>• `sigbands`: Return time signals (Default: False)<br>• `detrend`: Remove DC offset (Default: True)<br>• `calibration_factor`: Sensitivity multiplier (Default: 1.0)<br>• `dbfs`: Output in dBFS instead of dB SPL (Default: False)<br>• `mode`: 'rms' or 'peak' (Default: 'rms')<br>• `nominal`: IEC 61260-1 nominal labels (Default: False)<br>• `show`: Plot response (Default: False)<br>• `plot_file`: Path to save plot (Default: None)<br>• `ripple`: Passband ripple [dB] (for cheby1/ellip)<br>• `attenuation`: Stopband atten. [dB] (Default: 72; for cheby2/ellip — cheby2 needs >= 70 dB for class 1) | `spl, freq = octave_filter(x, fs, ...)`<br>• `spl`: levels [dB]<br>• `freq`: frequencies [Hz]<br><br>**With `sigbands=True`:**<br>`spl, freq, xb = octave_filter(x, fs, sigbands=True)`<br>• `xb`: List of filtered signals (one per band)<br><br>**Calibrated usage:**<br>`spl, f = octave_filter(x, fs, calibration_factor=0.05)` |
| `OctaveFilterBank` | `class` | **Efficient bank implementation.**<br>• `fs`: Sample rate [Hz]<br>• `fraction`: 1, 3, etc.<br>• `order`: Filter order<br>• `limits`: [f_min, f_max] (Default: [12, 20000])<br>• `filter_type`: Architecture name<br>• `show`: Plot response (Default: False)<br>• `plot_file`: Path to save the plot (Default: None)<br>• `calibration_factor`: Sensitivity multiplier<br>• `dbfs`: Use dBFS (Default: False)<br>• `stateful`: Carry filter state between calls (Default: False)<br>• `steady_ic`: Steady-state initial conditions (Default: False)<br>• `resample`: Multirate decimation (Default: True)<br>• `ripple`: Passband ripple [dB]<br>• `attenuation`: Stopband attenuation [dB] (Default: 72; cheby2 needs >= 70 dB for class 1) | `bank = OctaveFilterBank(fs=48000, fraction=3, order=6, filter_type='butter')`<br>`spl, f = bank.filter(x, sigbands=False, mode='rms', detrend=True, zero_phase=False)`<br><br>• `bank`: Instance of the filter bank<br>• `bank.freq` / `bank.freq_d` / `bank.freq_u` / `bank.sos`: computed properties |
| `OctaveFilterBank.spectrogram` | `method` | **Band levels over time.**<br>• `x`: Signal array (1D or 2D)<br>• `window_time`: Window length [s] (Default: 0.125)<br>• `overlap`: Fraction in [0, 1) (Default: 0.5)<br>• `mode`: 'rms' or 'peak'<br>• `zero_phase`: Group-delay-free frames (Default: False) | `levels, freq, times = bank.spectrogram(x)`<br><br>• `levels`: (bands, frames) or (channels, bands, frames)<br>• `times`: window centers [s] |
| `weighting_filter` | `function` | **Acoustic weighting.**<br>• `x`: Signal array<br>• `fs`: Sample rate [Hz]<br>• `curve`: 'A', 'C', 'G' (ISO 7196 infrasound) or 'Z' (Default: 'A')<br>• `high_accuracy`: IEC class 1 HF accuracy via internal oversampling (Default: True) | `y = weighting_filter(x, fs, curve='A')`<br><br>• `y`: weighted signal |
| `WeightingFilter` | `class` | **Reusable weighting filter.**<br>• `fs`: Sample rate [Hz]<br>• `curve`: 'A', 'C', 'G' or 'Z'<br>• `stateful`: Block processing (Default: False)<br>• `steady_ic`: Steady-state initial conditions (Default: False)<br>• `high_accuracy`: Defaults to True except stateful | `wf = WeightingFilter(fs, 'A')`<br>`y = wf.filter(x)` |
| `time_weighting` | `function` | **Energy capture.**<br>• `x`: Raw signal array (squared internally; time is the last axis)<br>• `fs`: Sample rate [Hz]<br>• `mode`: 'fast', 'slow', or 'impulse'<br>• `initial_state`: None, 'zero', 'first', scalar, or array (Default: None) | `env = time_weighting(x, fs, mode='fast')`<br><br>• `env`: energy envelope (Mean Square), same shape as `x` |
| `TimeWeighting` | `class` | **Stateful time weighting.**<br>• `fs`: Sample rate [Hz]<br>• `mode`: 'fast', 'slow', 'impulse' (Default: 'fast') | `tw = TimeWeighting(fs, mode='fast')`<br>`env = tw.process(block)` per block<br>`tw.reset()` to start over |
| `leq` | `function` | **Equivalent level (Leq).**<br>• `x`: Signal array (1D or 2D)<br>• `calibration_factor`: Sensitivity multiplier (Default: 1.0)<br>• `dbfs`: Output in dBFS (Default: False) | `level = leq(x, calibration_factor=s)`<br><br>• `level`: Scalar (1D) or per-channel array (2D) |
| `laeq` | `function` | **A-weighted Leq (LAeq).**<br>• `x`: Signal array (1D or 2D)<br>• `fs`: Sample rate [Hz]<br>• `calibration_factor` / `dbfs`: as `leq` | `level = laeq(x, fs, calibration_factor=s)`<br><br>• `level`: Scalar (1D) or per-channel array (2D) |
| `ln_levels` | `function` | **Statistical levels (LN).**<br>• `x`: Signal array (1D or 2D)<br>• `fs`: Sample rate [Hz]<br>• `n`: Exceedance percentiles (Default: (10, 50, 90))<br>• `mode`: 'fast', 'slow', 'impulse' (Default: 'fast')<br>• `weighting`: 'A', 'C', 'G', 'Z' or None (Default: None)<br>• `calibration_factor` / `dbfs`: as `leq` | `stats = ln_levels(x, fs, n=(10, 50, 90), weighting='A')`<br><br>• `stats`: Dict `{10: L10, 50: L50, 90: L90}` |
| `lc_peak` | `function` | **C-weighted peak (LCpeak).**<br>• `x`: Signal array (1D or 2D)<br>• `fs`: Sample rate [Hz]<br>• `calibration_factor`: as `leq`<br>• `dbfs`: 0 dBFS = full-scale *peak* (amplitude 1.0), unlike the RMS reference of `leq`<br>• `oversample`: HF inter-sample peak recovery (Default: 8; 1 = on-grid, under-reads up to ~1.15 dB at 48 kHz) | `peak = lc_peak(x, fs)`<br><br>• IEC 61672-1 §5.13; verified against Table 5 |
| `sel` | `function` | **Sound exposure level (SEL/LAE).**<br>• `x`: Whole-event signal (1D or 2D)<br>• `fs`: Sample rate [Hz]<br>• `weighting`: 'A', 'C', 'G', 'Z' or None (Default: None)<br>• `calibration_factor` / `dbfs`: as `leq` | `lae = sel(x, fs, weighting='A')`<br><br>• Event level normalized to 1 s |
| `sound_exposure` | `function` | **A-weighted exposure E (IEC 61252).**<br>• `x`: Signal (1D or 2D)<br>• `fs`: Sample rate [Hz]<br>• `duration_hours`: exposure period represented (Default: recording length)<br>• `calibration_factor` | `E = sound_exposure(x, fs, duration_hours=8)`<br><br>• `E`: Pa²·h |
| `lex_8h` | `function` | **Daily exposure LEX,8h / LEP,d.**<br>• Same params as `sound_exposure` | `lex = lex_8h(x, fs, duration_hours=4)`<br><br>• Normalized 8 h level [dB] |
| `loudness_zwicker` | `function` | **Zwicker loudness (ISO 532-1:2017).**<br>• `x`: Calibrated signal in Pa (1D)<br>• `fs`: Sample rate [Hz]<br>• `field`: 'free' or 'diffuse' (Default: 'free')<br>• `stationary`: Clause 5 stationary method (Default: False)<br>• `calibration_factor`: Digital units to Pa (Default: 1.0) | `res = loudness_zwicker(x, fs)`<br><br>• `ZwickerLoudness`; time-varying runs add N5/N10 and the 500 Hz N(t) trace |
| `loudness_zwicker_from_spectrum` | `function` | **Stationary loudness from band levels.**<br>• `levels`: 28 one-third-octave levels, 25 Hz-12.5 kHz [dB SPL]<br>• `field`: 'free' or 'diffuse' (Default: 'free') | `res = loudness_zwicker_from_spectrum(levels)`<br><br>• `res.loudness` [sone], `res.loudness_level` [phon] |
| `ZwickerLoudness` | `dataclass` | **Loudness result.**<br>• `loudness`: N [sone]<br>• `loudness_level`: LN [phon]<br>• `specific`: N′(z), 240 bins of 0.1 Bark<br>• `n5` / `n10`: percentile loudness (time-varying only)<br>• `time` / `loudness_vs_time`: 500 Hz trace | `res.loudness, res.n5`<br><br>• Time-varying fields are `None` for stationary results |
| `sharpness_din` | `function` | **Sharpness in acum (DIN 45692).**<br>• `x`: Signal (1D)<br>• `fs`: Sample rate [Hz]<br>• `field`: 'free' or 'diffuse' (Default: 'free')<br>• `method`: 'din', 'aures' or 'bismarck' (Default: 'din')<br>• `calibration_factor`: Digital units to Pa (Default: 1.0) | `s = sharpness_din(x, fs)`<br><br>• `s`: sharpness [acum] |
| `sharpness_din_from_specific` | `function` | **Sharpness from a specific-loudness pattern.**<br>• `specific`: N′(z), 240 values at 0.1 Bark (e.g. `ZwickerLoudness.specific`)<br>• `method`: 'din', 'aures' or 'bismarck' (Default: 'din') | `s = sharpness_din_from_specific(res.specific)`<br><br>• `s`: sharpness [acum] |
| `loudness_moore_glasberg` | `function` | **Moore-Glasberg loudness (ISO 532-2:2017).**<br>• `x`: Calibrated signal in Pa (1D)<br>• `fs`: Sample rate [Hz]<br>• `field`: 'free', 'diffuse' or 'eardrum' (Default: 'free')<br>• `presentation`: 'binaural'/'diotic' or 'monaural' (Default: 'binaural') | `res = loudness_moore_glasberg(x, fs)`<br><br>• `MooreGlasbergLoudness` (roex excitation pattern) |
| `loudness_moore_glasberg_from_spectrum` | `function` | **Exact loudness from sinusoidal components (ISO 532-2 §5.2/5.4).**<br>• `components`: sequence of (frequency [Hz], level [dB SPL]) pairs<br>• `field`: 'free'/'diffuse'/'eardrum' (Default: 'free')<br>• `presentation`: (Default: 'binaural') | `res = loudness_moore_glasberg_from_spectrum([(1000.0, 40.0)])`<br><br>• 1 kHz/40 dB → 1.000 sone |
| `loudness_moore_glasberg_from_third_octave` | `function` | **Loudness from 29 one-third-octave band levels (ISO 532-2 §5.5).**<br>• `band_levels`: 29 levels, 25 Hz–16 kHz [dB SPL]<br>• `field` / `presentation`: as above | `res = loudness_moore_glasberg_from_third_octave(levels)`<br><br>• `MooreGlasbergLoudness` |
| `MooreGlasbergLoudness` | `dataclass` | **Moore-Glasberg loudness result.**<br>• `loudness`: N [sone]<br>• `loudness_level`: LN [phon]<br>• `specific`: N′(i), 372 bins of 0.1 Cam<br>• `erb_number` / `centre_frequencies`: Cam / Hz axes<br>• `field` / `presentation`<br>• `.plot()`: specific loudness N′(i) over Cam | `res.loudness, res.loudness_level` |
| `loudness_moore_glasberg_time` | `function` | **Time-varying loudness (ISO 532-3:2023).**<br>• `signal`: Calibrated Pa; 1D (diotic) or (n, 2) ears<br>• `fs`: Sample rate [Hz]<br>• `field`: 'free'/'diffuse'/'eardrum' (Default: 'free')<br>• `presentation`: (Default: 'binaural')<br>• `percentiles`: exceedance % (Default: (1,5,10,50,90,95)) | `res = loudness_moore_glasberg_time(x, fs)`<br><br>• `MooreGlasbergTimeVaryingLoudness` |
| `MooreGlasbergTimeVaryingLoudness` | `dataclass` | **Time-varying loudness result.**<br>• `time`: 1 ms grid [s]<br>• `short_term_loudness` / `long_term_loudness`: S′(t)/S″(t) [sone]<br>• `short_term_loudness_level` / `long_term_loudness_level` [phon]<br>• `n_max` / `loudness_level_max`: peak long-term loudness<br>• `percentiles`: dict {percent: sone}<br>• `.plot()`: STL and LTL vs time | `res.n_max, res.percentiles[5.0]` |
| `loudness_ecma` | `function` | **Sottek Hearing Model loudness (ECMA-418-2:2025).**<br>• `signal_in`: Calibrated signal in Pa (1D)<br>• `fs`: Sample rate [Hz] (resampled to 48 kHz)<br>• `field`: 'free' or 'diffuse' (Default: 'free') | `res = loudness_ecma(x, fs)`<br><br>• `EcmaLoudness`; 1 kHz/40 dB ≈ 1 sone_HMS |
| `EcmaLoudness` | `dataclass` | **Sottek loudness result.**<br>• `loudness`: N [sone_HMS]<br>• `specific_loudness`: N′(z), 53 Bark_HMS bands<br>• `bark` / `centre_frequencies`: z / Hz axes<br>• `time` / `loudness_vs_time`: N(l) at 187.5 Hz<br>• `field`<br>• `.plot()`: N′(z) + N(l) | `res.loudness, res.specific_loudness` |
| `tonality_ecma` | `function` | **Sottek tonality (ECMA-418-2:2025).**<br>• `signal_in`: Calibrated signal in Pa (1D)<br>• `fs`: Sample rate [Hz] (resampled to 48 kHz)<br>• `field`: 'free' or 'diffuse' (Default: 'free')<br>• `f_low` / `f_high`: optional user band [Hz] (Default: None) | `res = tonality_ecma(x, fs)`<br><br>• `EcmaTonality`; 1 kHz/40 dB ≈ 1 tu_HMS |
| `EcmaTonality` | `dataclass` | **Sottek tonality result.**<br>• `tonality`: T [tu_HMS]<br>• `specific_tonality`: T′(z), 53 bands<br>• `tonal_frequencies`: f_ton,z per band [Hz]<br>• `bark` / `centre_frequencies`<br>• `time` / `tonality_vs_time` / `tonal_frequency_vs_time`: T(l), f_ton(l)<br>• `field`<br>• `.plot()`: T′(z) + T(l) | `res.tonality, res.tonal_frequencies` |
| `roughness_ecma` | `function` | **Sottek roughness (ECMA-418-2:2025), new capability.**<br>• `signal_in`: Calibrated signal in Pa (1D)<br>• `fs`: Sample rate [Hz] (resampled to 48 kHz)<br>• `field`: 'free' or 'diffuse' (Default: 'free') | `res = roughness_ecma(x, fs)`<br><br>• `EcmaRoughness`; 1 kHz/70 Hz/100 %-AM/60 dB ≈ 1 asper |
| `EcmaRoughness` | `dataclass` | **Sottek roughness result.**<br>• `roughness`: R [asper] (90th percentile of R(l50))<br>• `specific_roughness`: R′(z), 53 bands<br>• `bark` / `centre_frequencies`<br>• `time` / `roughness_vs_time`: R(l50) at 50 Hz<br>• `specific_roughness_vs_time`: (n_times, 53)<br>• `field`<br>• `.plot()`: R(l50) + specific-roughness heatmap | `res.roughness, res.specific_roughness` |
| `equal_loudness_contour` | `function` | **ISO 226:2023 equal-loudness contour.**<br>• `phon`: Loudness level, 20-90 phon | `freqs, spl = equal_loudness_contour(40.0)`<br><br>• SPL at the 29 preferred frequencies |
| `loudness_level` | `function` | **Loudness level of a pure tone (phon).**<br>• `spl`: Tone SPL [dB]<br>• `frequency`: One of the 29 Table 1 frequencies [Hz] | `phon = loudness_level(73.0, 63.0)` |
| `hearing_threshold` | `function` | **Threshold of hearing (ISO 226 Table 1).**<br>• (no parameters) | `freqs, tf = hearing_threshold()` |
| `tone_to_noise_ratio` | `function` | **Tone-to-noise ratio (ECMA-418-1 §11).**<br>• `x`: Signal (1D)<br>• `fs`: Sample rate [Hz]<br>• `tone_freq`: Tone to assess [Hz] (Default: highest peak)<br>• `resolution_hz`: FFT bin spacing (Default: 1.0) | `r = tone_to_noise_ratio(x, fs)`<br><br>• `ToneAssessment(frequency, ratio_db, criterion_db, prominent)` |
| `prominence_ratio` | `function` | **Prominence ratio (ECMA-418-1 §12).**<br>• Same params as `tone_to_noise_ratio` | `r = prominence_ratio(x, fs, tone_freq=1000)`<br><br>• `ToneAssessment(...)` |
| `ToneAssessment` | `dataclass` | **Tone prominence verdict.**<br>• `frequency`: Assessed tone [Hz]<br>• `ratio_db`: TNR or PR [dB]<br>• `criterion_db`: Prominence limit at that frequency [dB]<br>• `prominent`: bool | `r = tone_to_noise_ratio(x, fs)`<br>`if r.prominent: ...` |
| `sti_from_impulse_response` | `function` | **Full STI, indirect method (IEC 60268-16 Ed. 5).**<br>• `ir`: Impulse response (1D)<br>• `fs`: Sample rate [Hz] (>= 22500)<br>• `snr`: SNR [dB], scalar or 7 bands (Default: None)<br>• `level`: 7 speech band levels [dB SPL]; enables masking + reception threshold (Default: None)<br>• `ambient`: 7 noise band levels [dB SPL]; requires `level` | `res = sti_from_impulse_response(ir, fs, snr=25.0)`<br><br>• `STIResult` with `mtf` (7×14) |
| `stipa` | `function` | **STIPA direct method (Annex B).**<br>• `x`: Recorded STIPA signal (1D), 15-25 s<br>• `fs`: Sample rate [Hz] (>= 22500)<br>• `reference`: Measured source signal instead of the nominal m = 0.55 (Default: None)<br>• `level` / `ambient`: as `sti_from_impulse_response`<br>• warns (`UserWarning`) if the recording is < 15 s (STI biased low) | `res = stipa(recording, fs)`<br><br>• `STIResult` with `mtf` (7×2) |
| `stipa_signal` | `function` | **STIPA test-signal generator (A.4/A.6.1).**<br>• `fs`: Sample rate [Hz] (>= 22500)<br>• `seconds`: Duration [s] (Default: 18.0)<br>• `level_db`: RMS level [dB SPL] (Default: None → RMS 0.1)<br>• `seed`: Pink-noise seed (Default: None) | `sig = stipa_signal(48000, seconds=18.0)`<br><br>• 1D test signal, Ed. 5 male spectrum |
| `STIResult` | `dataclass` | **STI result.**<br>• `sti`: 0 to 1<br>• `mti`: band indices (7,)<br>• `mtf`: corrected m values (7×14 or 7×2)<br>• `band_levels`: levels used or None<br>• `rating`: Annex F letter 'A+'…'U' | `res = stipa(x, fs)`<br>`print(res.sti, res.rating)` |
| `sound_intensity` | `function` | **p-p sound intensity (IEC 61043).**<br>• `p1`, `p2`: Microphone signals [Pa], equal length<br>• `fs`: Sample rate [Hz]<br>• `spacing`: Microphone separation Δr [m]<br>• `rho`: Air density (Default: 1.204)<br>• `c`: Speed of sound (Default: 343.0)<br>• `fraction`: None, 1 or 3 (Default: None)<br>• `limits`: [f_min, f_max] (Default: [12, 20000])<br>• `bias_correct`: undo finite-difference under-read of band/broadband totals near `max_valid_frequency` (Default: False) | `res = sound_intensity(p1, p2, fs, spacing=0.012, fraction=3)`<br><br>• `IntensityResult` |
| `IntensityResult` | `dataclass` | **Intensity result.**<br>• Per band (with `fraction`): `frequency`, `intensity` [W/m²], `intensity_level`, `pressure_level`, `pressure_intensity_index`, `direction` (±1), `bias_correction`<br>• Broadband: `total_*` counterparts<br>• `max_valid_frequency`: 0.1·c/Δr | `res.total_intensity_level`<br>`res.total_direction` |
| `field_indicators` | `function` | **ISO 9614-1 Annex A field indicators.**<br>• `pressure_levels`: Lpi per position [dB]<br>• `normal_intensity`: Signed Ini per position [W/m²] | `fi = field_indicators(lp, i_n)`<br><br>• `FieldIndicators(f2, f3, f4)` |
| `FieldIndicators` | `dataclass` | **ISO 9614-1 Annex A indicators.**<br>• `f2`: surface pressure-intensity indicator (Eq. A.3)<br>• `f3`: negative partial power indicator (Eq. A.6)<br>• `f4`: field non-uniformity indicator (Eq. A.8)<br>• f3 − f2 > 0 reveals negative partial power | `fi.f2, fi.f3, fi.f4`<br><br>• Criteria: Ld > F2, N > C·F4² |
| `dynamic_capability_index` | `function` | **Dynamic capability Ld (ISO 9614-1 §3.12).**<br>• `pressure_residual_intensity_index`: δpI0 [dB]<br>• `bias_error_factor`: K [dB] (Default: 10.0) | `ld = dynamic_capability_index(18.0)`<br><br>• Adequate when `Ld > F2` (criterion 1) |
| `CalibrationWarning` | `warning class` | **Unreliable calibration recording.**<br>Emitted by `sensitivity` — with `fs` given and `validate=True` — when the tone is unstable (IEC 60942 limit) or too short | `warnings.simplefilter("error", CalibrationWarning)` |
| `lden` | `function` | **Day-evening-night level (ISO 1996-1 §3.6.4).**<br>• `lday`/`levening`/`lnight`: LAeq per period [dB]<br>• `hours`: Period durations (Default: (12, 4, 8)) | `l = lden(63.2, 58.1, 51.4)` |
| `ldn` | `function` | **Day-night level (ISO 1996-1 §3.6.5).**<br>• `lday`/`lnight`: LAeq per period [dB]<br>• `hours`: Default (15, 9) | `l = ldn(63.2, 51.4)` |
| `composite_rating_level` | `function` | **Whole-day composite rating (ISO 1996-1 §6.5).**<br>• `periods`: list of (level_db, hours, adjustment_db) summing 24 h | `r = composite_rating_level([(63, 12, 0), (58, 4, 5), (51, 8, 10)])` |
| `linkwitz_riley` | `function` | **Audio crossover.**<br>• `x`: Signal array<br>• `fs`: Sample rate [Hz]<br>• `freq`: Crossover frequency [Hz]<br>• `order`: Any even number (Default: 4) | `lo, hi = linkwitz_riley(x, fs, freq=1000, order=4)`<br><br>• `lo`: Low-pass filtered signal<br>• `hi`: High-pass filtered signal |
| `sensitivity` | `function`| **SPL Calibration.**<br>• `ref_signal`: Calibration signal<br>• `target_spl`: Level of calibrator (Default: 94.0)<br>• `ref_pressure`: Reference pressure (Default: 20e-6)<br>• `narrowband`: coherent Goertzel tone estimate that rejects broadband hum/noise (needs `fs`; Default: False) | `s = sensitivity(ref_signal, target_spl=94.0)`<br><br>• `s`: Float (multiplier for pressure) |
| `verify_filter_class` | `function` | **IEC 61260-1:2014 class check.**<br>• `bank`: an `OctaveFilterBank`<br>• `num_points`: frequency grid points per band (Default: 32768) | `result = verify_filter_class(bank)`<br><br>• `result["overall_class"]`: 1, 2 or None<br>• `result["bands"]`: per-band class and margins [dB] |
| `class_limits` | `function` | **IEC 61260-1:2014 Table 1 acceptance limits.**<br>• `fraction`: bandwidth designator denominator b (1, 3, ...)<br>• `filter_class`: 1 or 2<br>• `omega`: normalized frequencies f/fm | `lo, hi = class_limits(3, 1, omega)`<br><br>• `lo` / `hi`: min/max relative attenuation [dB] (`hi` is `inf` outside the pass-band) |
| `nominal_frequencies` | `function` | **ANSI Frequency generator.**<br>• `fraction`: 1, 3, etc. (Required)<br>• `limits`: [f_min, f_max] (Default: [12, 20000]) | `f_cen, f_low, f_high, labels = nominal_frequencies(fraction=3)`<br><br>• `f_cen`: List of center frequencies [Hz]<br>• `f_low`: List of lower edges [Hz]<br>• `f_high`: List of upper edges [Hz]<br>• `labels`: IEC nominal frequency labels |
| `normalized_frequencies` | `function` | **Standard IEC Frequencies.**<br>• `fraction`: 1 or 3 | `freqs = normalized_frequencies(fraction=3)`<br><br>• `freqs`: List of standard center frequencies [Hz] |
| `sweep_signal` | `function` | **ESS excitation (ISO 18233 Annex B).**<br>• `fs`: Sample rate [Hz]<br>• `f1`: Start frequency [Hz]<br>• `f2`: Stop frequency [Hz] (≤ fs/2)<br>• `seconds`: Duration [s]<br>• `amplitude`: Peak (Default: 1.0)<br>• `fade`: Half-Hann fraction (Default: 0.01) | `s = sweep_signal(48000, 20, 20000, 3.0)`<br><br>• 1D exponential sine sweep |
| `inverse_filter` | `function` | **Farina inverse filter for an ESS.**<br>• Same parameters as `sweep_signal` | `inv = inverse_filter(48000, 20, 20000, 3.0)`<br><br>• Time-reversed, +6 dB/oct compensated sweep |
| `impulse_response` | `function` | **Sweep deconvolution (ISO 18233 B.5).**<br>• `recorded`: Recorded response (1D)<br>• `reference`: Emitted sweep (1D)<br>• `fs`: Sample rate [Hz]<br>• `method`: 'spectral' (Default) or 'farina'<br>• `f_range`: (f1, f2) for 'farina'<br>• `regularization`: Tikhonov term (Default: 1e-6)<br>• `length`: causal samples (Default: len(recorded))<br>• `return_full`: keep distortion tail (Default: False) | `ir = impulse_response(rec, sweep, fs)`<br><br>• `ImpulseResponseResult` (array-like; `.plot()`) |
| `mls_signal` | `function` | **Maximum-length sequence (ISO 18233 Annex A).**<br>• `order`: Register length N, 2-20 | `mls = mls_signal(16)`<br><br>• Bipolar sequence, length 2**N − 1 |
| `mls_impulse_response` | `function` | **IR from a periodic MLS.**<br>• `recorded`: Response spanning whole MLS periods (1D)<br>• `mls`: Excitation sequence<br>• `length`: IR samples (Default: 2**N − 1)<br>• `fs`: optional sample rate for the plot time axis | `ir = mls_impulse_response(rec, mls)`<br><br>• `ImpulseResponseResult` (array-like; `.plot()`) |
| `ImpulseResponseResult` | `dataclass` | **Recovered impulse response with metadata.**<br>• `ir`: IR samples<br>• `fs` [Hz] or None (e.g. an MLS recovery without one)<br>• `method`: 'spectral'/'farina'/'mls'<br>• array-like: `np.asarray(res)`, indexing, `len()` and `shape`/`dtype` forward to `ir`<br>• `.plot()` | `ir = impulse_response(rec, sweep, fs)`<br>`room_parameters(ir, fs)  # drop-in array` |
| `ImpulseResponseWarning` | `warning class` | **Suspect recovered impulse response.**<br>Emitted e.g. for MLS aliasing in the recovery | `warnings.simplefilter('error', ImpulseResponseWarning)` |
| `plot_excitation` | `function` | **Plot an excitation signal.**<br>• `signal`: sweep or MLS samples (1D)<br>• `fs`: Sample rate [Hz]<br>• `kind`: `'sweep'` (default) or `'mls'` | `plot_excitation(sweep, fs, kind="sweep")`<br><br>• waveform + spectrogram / spectrum axes |
| `decay_curve` | `function` | **Schroeder decay curve (ISO 3382-1 5.3.3).**<br>• `ir`: Impulse response (1D)<br>• `fs`: Sample rate [Hz]<br>• `band`: Band centre [Hz] (Default: None → broadband)<br>• `fraction`: 1 or 3 (Default: 1)<br>• `zero_phase`: forward-backward band filtering, halves the 125 Hz short-T bias (Default: False) | `dc = decay_curve(ir, fs)` → `DecayCurve`<br>`time, level = dc` still unpacks (`time` [s], `level` [dB], 0 dB at t=0)<br>`dc.plot()` draws the decay + EDT/T20/T30 fits |
| `DecayCurve` | `dataclass` | **Schroeder decay curve (ISO 3382-1 5.3.3).**<br>• `time`: from the direct sound [s]<br>• `level`: decay [dB], 0 dB at t = 0, up to the noise truncation point<br>• `band`: centre [Hz] or None (broadband)<br>• iterable: unpacks as `time, level`<br>• `.plot()`: decay + EDT/T20/T30 fits | `dc = decay_curve(ir, fs)`<br>`dc.time, dc.level, dc.band` |
| `room_parameters` | `function` | **Room acoustics (ISO 3382-1/2).**<br>• `ir`: Impulse response (1D)<br>• `fs`: Sample rate [Hz]<br>• `limits`: (f_min, f_max) or None (Default: (125, 4000))<br>• `fraction`: 1 or 3 (Default: 1)<br>• `zero_phase`: forward-backward octave filtering, halves the 125 Hz short-T T30 bias (Default: False) | `res = room_parameters(ir, fs)`<br><br>• `RoomAcousticsResult` per band |
| `RoomAcousticsResult` | `dataclass` | **Per-band room parameters.**<br>• `frequency` [Hz]<br>• `edt`, `t20`, `t30` [s]<br>• `c50`, `c80` [dB], `d50`, `ts` [s]<br>• `dynamic_range` [dB]<br>• `edt_valid`/`t20_valid`/`t30_valid`<br>• `curvature` [%] | `res.t30, res.c80, res.t30_valid`<br><br>• Arrays with one entry per band |
| `open_plan_metrics` | `function` | **Open-plan office metrics (ISO 3382-3).**<br>• `positions_m`: Source distances [m] (≥ 4)<br>• `spl_a_speech`: A-weighted speech level per position [dB]<br>• `sti_values`: STI per position | `m = open_plan_metrics(r, lp, sti)`<br><br>• `OpenPlanResult` |
| `OpenPlanResult` | `dataclass` | **Open-plan single numbers.**<br>• `d2s`: Spatial decay rate [dB/doubling]<br>• `lp_as_4m`: Speech level at 4 m [dB]<br>• `rd`: Distraction distance [m]<br>• `rp`: Privacy distance [m] | `m.d2s, m.rd, m.rp`<br><br>• `nan` when undefined |
| `airborne_insulation` | `function` | **Field airborne insulation (ISO 16283-1).**<br>• `l1`/`l2`: Source/receiving levels [dB], 1D or (positions, bands)<br>• `t2`: Receiving-room T per band [s]<br>• `area`: Partition S [m²] (for R')<br>• `volume`: Receiving V [m³] (for R')<br>• `t0`: Reference T0 [s] (Default: 0.5) | `ins = airborne_insulation(l1, l2, t2, area=10, volume=50)`<br><br>• `AirborneInsulationResult` |
| `weighted_rating` | `function` | **Single-number rating + C/Ctr (ISO 717-1).**<br>• `values_by_band`: 16 thirds or 5 octaves [dB]<br>• `bands`: 'third-octave', 'octave' or None | `w = weighted_rating(R)`<br><br>• `WeightedRatingResult` (Rw, C, Ctr) |
| `energy_average_level` | `function` | **Energy-average level (ISO 16283-1 (9)).**<br>• `levels`: Levels [dB] to average<br>• `axis`: Averaging axis (Default: -1) | `L = energy_average_level([60, 66])`<br><br>• `10 lg( mean(10^(Li/10)) )` |
| `AirborneInsulationResult` | `dataclass` | **Field insulation per band.**<br>• `d`: Level difference D [dB]<br>• `dnt`: Standardized DnT [dB]<br>• `r_prime`: Apparent R' [dB] or None | `res.d, res.dnt, res.r_prime` |
| `WeightedRatingResult` | `dataclass` | **Weighted rating result.**<br>• `rating`: Rw/DnT,w … [dB], int<br>• `c`: Spectrum term C, int<br>• `ctr`: Spectrum term Ctr, int<br>• `unfavourable_sum`: [dB]<br>• `band_centers`: Measured-curve centres [Hz] or None<br>• `measured`: Measured band values [dB] or None<br>• `shifted_reference`: Shifted Table 3 reference [dB] or None | `w.rating, w.c, w.ctr` |
| `impact_insulation` | `function` | **Field impact insulation (ISO 16283-2).**<br>• `li`: Impact SPL [dB], 1D or (positions, bands)<br>• `t2`: Receiving-room T per band [s]<br>• `volume`: Receiving V [m³] (for L'n)<br>• `t0`: Reference T0 [s] (Default: 0.5) | `imp = impact_insulation(li, t2, volume=50)`<br><br>• `ImpactInsulationResult` (`l_n_t`, `l_n`) |
| `weighted_impact_rating` | `function` | **Single-number impact rating + CI (ISO 717-2).**<br>• `values_by_band`: 16 thirds (100-3150 Hz) or 5 octaves (125-2000 Hz) [dB]<br>• `bands`: 'third-octave', 'octave' or None | `r = weighted_impact_rating(imp.l_n_t)`<br><br>• `ImpactRatingResult` (Ln,w, CI); octave rating carries the -5 dB rule |
| `ImpactInsulationResult` | `dataclass` | **Impact insulation per band.**<br>• `l_n_t`: Standardized L'nT [dB]<br>• `l_n`: Normalized L'n [dB] or None | `imp.l_n_t, imp.l_n` |
| `ImpactRatingResult` | `dataclass` | **Weighted impact rating.**<br>• `rating`: Ln,w/L'n,w/L'nT,w [dB], int<br>• `ci`: Spectrum term CI, int<br>• `unfavourable_sum`: [dB]<br>• `band_centers`: Measured-curve centres [Hz] or None<br>• `measured`: Measured impact levels [dB] or None<br>• `shifted_reference`: Shifted impact reference [dB] or None | `r.rating, r.ci` |
| `facade_insulation` | `function` | **Field façade insulation (ISO 16283-3).**<br>• `l1_2m`/`l2`: Level 2 m in front / receiving levels [dB], 1D or (positions, bands)<br>• `t2`: Receiving-room T per band [s]<br>• `area`: Element S [m²], `volume`: Receiving V [m³], `surface_level`: L1,s [dB] (all three for R')<br>• `method`: 'loudspeaker' (−1.5 dB) / 'road_traffic' (−3 dB)<br>• `t0`: Reference T0 [s] (Default: 0.5)<br>• `frequencies` [Hz] | `fac = facade_insulation(l1_2m, l2, t2, volume=50, area=11.5, surface_level=ls)`<br><br>• `FacadeInsulationResult` |
| `FacadeInsulationResult` | `dataclass` | **Façade insulation per band.**<br>• `d_2m`: Level difference D2m [dB]<br>• `d_2m_nt`: Standardized D2m,nT [dB]<br>• `d_2m_n`: Normalized D2m,n [dB] or None<br>• `r_prime`: Apparent R'45°/R'tr,s [dB] or None<br>• `frequencies` [Hz] or None<br>• `.plot()` | `fac.d_2m_nt, fac.r_prime` |
| `lab_airborne_insulation` | `function` | **Laboratory airborne insulation (ISO 10140-2).**<br>• `l1`/`l2`: Source/receiving levels [dB], 1D or (positions, bands)<br>• `t2`: Receiving-room T per band [s]<br>• `area`: Free test-opening S [m²]<br>• `volume`: Receiving V [m³] | `lab = lab_airborne_insulation(l1, l2, t2, area=10, volume=50)`<br><br>• `LabAirborneInsulationResult` |
| `lab_impact_insulation` | `function` | **Laboratory impact insulation (ISO 10140-3).**<br>• `li`: Tapping-machine impact SPL [dB], 1D or (positions, bands)<br>• `t2`: Receiving-room T per band [s]<br>• `volume`: Receiving V [m³] | `imp = lab_impact_insulation(li, t2, volume=50)`<br><br>• `LabImpactInsulationResult` |
| `background_correction` | `function` | **Background-noise correction (ISO 10140-4 §4.3).**<br>• `signal_and_background`: Combined Lsb per band [dB]<br>• `background`: Lb per band [dB]<br>• 6–15 dB margin corrected, ≤6 dB capped at 1.3 dB, ≥15 dB unchanged | `L = background_correction(lsb, lb)`<br><br>• Corrected levels [dB] (`LabInsulationWarning` at the limit of measurement) |
| `LabAirborneInsulationResult` | `dataclass` | **Laboratory airborne result.**<br>• `r`: Sound reduction index R [dB]<br>• `absorption`: A = 0.16 V/T [m²]<br>• `rating`: `WeightedRatingResult` or None<br>• `.plot()` (needs the rating) | `lab.r, lab.rating.rating` |
| `LabImpactInsulationResult` | `dataclass` | **Laboratory impact result.**<br>• `l_n`: Normalized impact level Ln [dB]<br>• `absorption`: A [m²]<br>• `rating`: `ImpactRatingResult` or None<br>• `.plot()` (needs the rating) | `imp.l_n, imp.rating.rating` |
| `LabInsulationWarning` | `warning class` | **Limit-of-measurement condition (ISO 10140-4).**<br>Emitted by `background_correction` when a band's signal-to-background margin is ≤ 6 dB (fixed 1.3 dB cap applied) | `warnings.simplefilter('error', LabInsulationWarning)` |
| `predicted_airborne_insulation` | `function` | **Predicted apparent airborne R'w (EN 12354-1 Formula 26).**<br>• `r_direct`: Separating-element Rs,w [dB]<br>• `flanking_paths`: sequence of `FlankingPath` (Default: ())<br>• `delta_r_direct`: Lining ΔRDd,w [dB] (Default: 0) | `res = predicted_airborne_insulation(r_direct=57, flanking_paths=paths)`<br><br>• `AirbornePredictionResult` |
| `predicted_impact_insulation` | `function` | **Predicted apparent impact L'n,w (EN 12354-2 Formula 21).**<br>• `ln_w_eq`: Bare-floor equivalent Ln,w,eq [dB]<br>• `delta_l_w`: Covering improvement ΔLw [dB] (Default: 0)<br>• `k_correction`: Flanking K [dB] (Default: 0) | `imp = predicted_impact_insulation(ln_w_eq=76.2, delta_l_w=33, k_correction=2)`<br><br>• `ImpactPredictionResult` |
| `junction_vibration_reduction` | `function` | **Vibration reduction index Kij (EN 12354-1 Annex E).**<br>• `junction_type`: 'rigid_cross'/'rigid_t'/'flexible_t'/'lightweight_facade'<br>• `path`: 'through' (K13) / 'corner' (K12=K23)<br>• `mass_ratio`: m'⊥,i/m'i<br>• `frequency` [Hz] (Default: 500), `f1` [Hz] (Default: 125) | `k = junction_vibration_reduction('rigid_cross', 'through', 1.61)`<br><br>• Kij [dB] |
| `junction_min_vibration_reduction` | `function` | **Minimum Kij,min (EN 12354-1 Formula 29).**<br>• `coupling_length`: lf [m]<br>• `s_i`, `s_j`: Element areas [m²] | `kmin = junction_min_vibration_reduction(4.5, 11.5, 11.5)`<br><br>• Kij,min [dB] |
| `flanking_path` | `function` | **One flanking path Rij,w (EN 12354-1 Formula 28a).**<br>• `label`, `kind`: 'Ff'/'Df'/'Fd'<br>• `r_source`/`r_receive`: element indices [dB]<br>• `k_ij` [dB], `separating_area` Ss [m²], `coupling_length` lf [m]<br>• `delta_r` [dB] (Default: 0), `kij_min` [dB] clamp (Default: None) | `p = flanking_path(label='f', kind='Ff', r_source=49, r_receive=49, k_ij=12.4, separating_area=11.5, coupling_length=4.5)`<br><br>• `FlankingPath` |
| `flanking_element` | `function` | **The three paths (Ff, Df, Fd) of one flanking element.**<br>• `label`, `r_flanking`, `r_separating` [dB]<br>• `k_ff`/`k_fd`/`k_df` [dB]<br>• `separating_area` Ss [m²], `coupling_length` lf [m]<br>• `delta_r_ff`/`delta_r_fd`/`delta_r_df` [dB] (Default: 0) | `ff, df, fd = flanking_element(label='floor', r_flanking=49, r_separating=57, k_ff=12.4, k_fd=8.9, k_df=8.9, separating_area=11.5, coupling_length=4.5)` |
| `combine_linings` | `function` | **Combine two lining improvements (EN 12354-1 Formulas 30/31).**<br>• `delta_a`, `delta_b` [dB] (pass 0 for a single lining) | `dr = combine_linings(14.0, 14.0)`<br><br>• max(a,b) + min(a,b)/2 = 21.0 [dB] |
| `equivalent_impact_level` | `function` | **Bare-floor equivalent Ln,w,eq (EN 12354-2 Annex B).**<br>• `mass_per_area`: m' [kg/m²] | `lneq = equivalent_impact_level(322.0)`<br><br>• 164 − 35 lg(m') = 76.2 [dB] |
| `impact_flanking_correction` | `function` | **Flanking correction K (EN 12354-2 Table 1).**<br>• `separating_mass`, `flanking_mass` [kg/m²] (nearest tabulated) | `k = impact_flanking_correction(322.0, 145.0)`<br><br>• K = 2 [dB], int |
| `standardized_impact_level` | `function` | **Standardized L'nT,w (EN 12354-2 Formula 3).**<br>• `l_prime_n_w`: L'n,w [dB]<br>• `volume`: Receiving V [m³], V0 = 30 m³ | `lnt = standardized_impact_level(45.2, 50.0)`<br><br>• L'nT,w = 43.0 [dB] |
| `AirbornePredictionResult` | `dataclass` | **Predicted airborne insulation.**<br>• `r_prime_w`: Apparent R'w [dB]<br>• `r_direct_w`: Direct RDd,w [dB]<br>• `paths`: tuple of `PathContribution`<br>• `dominant`: highest-energy path | `res.r_prime_w, res.dominant.label` |
| `ImpactPredictionResult` | `dataclass` | **Predicted impact insulation.**<br>• `l_prime_n_w`: Apparent L'n,w [dB]<br>• `ln_w_eq`, `delta_l_w`, `k_correction` [dB] | `imp.l_prime_n_w` |
| `FlankingPath` | `dataclass` | **One flanking transmission path.**<br>• `label`, `kind`: 'Ff'/'Df'/'Fd'<br>• `r_ij_w`: Flanking index Rij,w [dB] | `p.r_ij_w` |
| `PathContribution` | `dataclass` | **A path with its energy share.**<br>• `label`, `kind`: 'Dd'/'Ff'/'Df'/'Fd'<br>• `r_w`: Path index [dB]<br>• `fraction`: share of transmitted energy (0–1) | `c.r_w, c.fraction` |
| `band_uncertainty` | `function` | **One-third-octave standard uncertainty u (ISO 12999-1 Tables 2/4/6).**<br>• `measurand`: 'airborne'/'impact'/'impact_reduction'<br>• `situation`: 'A'/'B'/'C'<br>• `upper_limit`: σR95 (airborne A, Annex D) (Default: False) | `u = band_uncertainty('airborne', 'B')`<br><br>• `BandUncertainty` |
| `single_number_uncertainty` | `function` | **Single-number standard uncertainty u (ISO 12999-1 Tables 3/5/7).**<br>• `quantity`: 'r_w'/'ln_w'/'delta_lw' (+ aliases, +c/+ctr variants)<br>• `situation`: 'A'/'B'/'C'<br>• `upper_limit` (Default: False) | `u = single_number_uncertainty('r_w', 'B')`<br><br>• u [dB] (0.9) |
| `single_number_uncertainty_uncorrelated` | `function` | **Uncorrelated single-number u from bands (ISO 12999-1 Formula B.2).**<br>• `band_uncertainties`: per-band u_i [dB]<br>• `reference_differences`: L_i − R_i [dB] | `u = single_number_uncertainty_uncorrelated(u_i, d_i)`<br><br>• Energy-weighted quadrature u [dB] |
| `maximum_repeatability_standard_deviation` | `function` | **Max repeatability σx per band (ISO 12999-1 Table 1).**<br>• (no parameters) | `b = maximum_repeatability_standard_deviation()`<br><br>• `BandUncertainty` (lab self-verification) |
| `insulation_coverage_factor` | `function` | **Coverage factor k (ISO 12999-1 Table 8).**<br>• `confidence`: fraction (Default: 0.95)<br>• `one_sided` (Default: False) | `k = insulation_coverage_factor(0.95)`<br><br>• 1.96 (two-sided) / 1.65 (one-sided) |
| `insulation_expanded_uncertainty` | `function` | **Expanded uncertainty U = k·u (ISO 12999-1 Formula 2).**<br>• `u` [dB]<br>• `coverage`: fraction (Default: 0.95)<br>• `one_sided` (Default: False); enforces k ≥ 1 | `U = insulation_expanded_uncertainty(0.9)`<br><br>• 1.764 [dB] |
| `uncertain_value` | `function` | **Attach U to a rating (ISO 12999-1 Clause 8).**<br>• `value` [dB], `quantity`, `situation`<br>• `coverage` (Default: 0.95), `one_sided` (Default: False), `upper_limit` (Default: False) | `uv = uncertain_value(52.0, 'rprime_w', 'B')`<br><br>• `UncertainValue` (value ± U) |
| `combine_uncertainties` | `function` | **Quadrature combination (ISO 12999-1 Formula C.2).**<br>• `*components`: non-negative u_i [dB] | `uc = combine_uncertainties(1.0, 0.6)`<br><br>• sqrt(Σ u_i²) = 1.166 [dB] |
| `prediction_input_uncertainty` | `function` | **Prediction input uncertainty (ISO 12999-1 Formula A.1).**<br>• `sigma_reproducibility`, `sigma_product` [dB]<br>• `n`: measurements (≥ 1) | `u = prediction_input_uncertainty(1.8, 1.0, 3)`<br><br>• sqrt((σR²+σp²)/n + σp²) [dB] |
| `reduce_by_independent_measurements` | `function` | **Reduce u by m measurements (ISO 12999-1 Formula A.7).**<br>• `u` [dB]<br>• `m`: independent measurements (≥ 1) | `ur = reduce_by_independent_measurements(1.0, 4)`<br><br>• u/√m = 0.5 [dB] |
| `satisfies_lower_requirement` | `function` | **Conformity to a minimum (ISO 12999-1 Formula 5).**<br>• `value`, `expanded_uncertainty_value`, `requirement` [dB] | `ok = satisfies_lower_requirement(52.0, 1.485, 50.0)`<br><br>• True when value − U > requirement |
| `satisfies_upper_requirement` | `function` | **Conformity to a maximum (ISO 12999-1 Formula 4).**<br>• `value`, `expanded_uncertainty_value`, `requirement` [dB] | `ok = satisfies_upper_requirement(45.0, 1.5, 50.0)`<br><br>• True when value + U < requirement |
| `BandUncertainty` | `dataclass` | **Per-band standard uncertainty (ISO 12999-1).**<br>• `measurand`, `situation`<br>• `frequencies` [Hz], `uncertainties` [dB]<br>• `upper_limit`: σR95 flag<br>• `.to_arrays()` | `b.frequencies, b.uncertainties` |
| `UncertainValue` | `dataclass` | **A value with its expanded uncertainty.**<br>• `value`, `standard_uncertainty`, `expanded_uncertainty` [dB]<br>• `coverage_factor`, `confidence`, `one_sided`<br>• `.lower` = y − U, `.upper` = y + U | `uv.lower, uv.upper` |
| `COVERAGE_FACTORS` | `mapping` | **Table 8 coverage factors (read-only).**<br>Keyed by `(confidence, one_sided)` → k | `COVERAGE_FACTORS[(0.95, False)]  # 1.96` |
| `sound_power_pressure` | `function` | **Sound power from surface pressure (ISO 3744/3746).**<br>• `levels_positions`: (NM, NB) SPL [dB]<br>• `surface`: 'hemisphere' / 'box'<br>• `radius` [m] or `dimensions`+`distance` [m]<br>• `reflecting_planes`: 1/2/3 (Default: 1)<br>• `background_levels`: for K1<br>• `frequencies` [Hz]: for LWA<br>• `reverberation_time`+`volume` / `absorption_area` / `mean_absorption_coefficient`+`room_surface`: for K2<br>• `grade`: 'engineering' (Default) / 'survey'<br>• `omc_uncertainty` [dB] (Default: 0) | `res = sound_power_pressure(levels, 'hemisphere', radius=1.5, frequencies=f)`<br><br>• `SoundPowerResult` |
| `measurement_positions` | `function` | **Hemisphere mic coordinates (ISO 3744 Annex B).**<br>• `surface`: 'hemisphere'<br>• `radius` [m]<br>• `reflecting_planes`: 1/2/3<br>• `tones`: Table B.1 vs B.2 (Default: True)<br>• `grade`: 'engineering'/'survey' | `xyz = measurement_positions('hemisphere', radius=1.5)`<br><br>• (N, 3) coordinates [m] |
| `background_noise_correction` | `function` | **Background correction K1 (ISO 3744 Eq. 16).**<br>• `source_levels` [dB]<br>• `background_levels` [dB]<br>• `grade`: 'engineering'/'survey' | `k1 = background_noise_correction(src, bg)`<br><br>• K1 per band [dB] |
| `environmental_correction` | `function` | **Environmental correction K2 (ISO 3744 Eq. A.2).**<br>• `surface_area` S [m²]<br>• `absorption_area` A, or `reverberation_time`+`volume`, or `mean_absorption_coefficient`+`room_surface` | `k2 = environmental_correction(14.1, reverberation_time=0.6, volume=300)`<br><br>• K2 [dB] |
| `SoundPowerResult` | `dataclass` | **Surface-pressure sound power.**<br>• `sound_power_level` [dB]<br>• `surface_pressure_level`, `mean_pressure_level` [dB]<br>• `background_correction`, `environmental_correction` [dB]<br>• `directivity_index` [dB] `(NM, NB)`<br>• `surface_area` [m²]<br>• `sound_power_level_a` [dB]<br>• `uncertainty` [dB]<br>• `grade` | `res.sound_power_level, res.sound_power_level_a` |
| `sound_power_reverberation` | `function` | **Reverberation-room LW, direct (ISO 3741).**<br>• `levels`: mean room SPL [dB] (1D or (NM, NB))<br>• `t60` [s]<br>• `volume` V [m³]<br>• `surface_area` S [m²]<br>• `frequencies` [Hz] (required)<br>• `background_levels`: for K1<br>• `temperature` [°C] (Default: 23)<br>• `static_pressure` [kPa] (Default: 101.325) | `rev = sound_power_reverberation(lp, t60, 200, 220, f)`<br><br>• `ReverberationSoundPowerResult` |
| `sound_power_comparison` | `function` | **Reverberation-room LW, comparison (ISO 3741).**<br>• `levels`, `levels_ref`: room SPL [dB]<br>• `lw_ref`: reference-source LW [dB]<br>• `frequencies` [Hz]<br>• `background_levels`, `background_levels_ref`<br>• `temperature`, `static_pressure` | `cmp = sound_power_comparison(lp, lp_ref, lw_ref)`<br><br>• `ReverberationSoundPowerResult` (method='comparison') |
| `ReverberationSoundPowerResult` | `dataclass` | **Reverberation-room sound power.**<br>• `frequencies` [Hz] (or `None`)<br>• `sound_power_level` [dB]<br>• `mean_pressure_level` [dB]<br>• `absorption_area` [m²]<br>• `waterhouse_correction` [dB]<br>• `background_correction`, `c1`, `c2` [dB]<br>• `speed_of_sound` [m/s]<br>• `sound_power_level_a` [dB]<br>• `method` | `rev.sound_power_level, rev.waterhouse_correction` |
| `sound_power_intensity` | `function` | **Sound power by intensity scanning (ISO 9614-2).**<br>• `normal_intensity`: (N_seg, N_bands) [W/m²]<br>• `areas`: segment Si [m²]<br>• `normal_intensity_2`: 2nd sweep (criterion 3)<br>• `pressure_levels`: for FpI<br>• `pressure_residual_index`: δpI0 [dB]<br>• `frequencies` [Hz]<br>• `band_type`: 'third' (Default)/'octave'<br>• `grade`: 'engineering'/'survey'<br>• `repeatability_limit`: override s | `ir = sound_power_intensity(scan1, areas, frequencies=f, band_type='octave')`<br><br>• `SoundPowerIntensityResult` |
| `SoundPowerIntensityResult` | `dataclass` | **Scanning sound power.**<br>• `partial_power`, `partial_power_level`<br>• `sound_power`, `sound_power_level` [dB] (NaN where `negative_band`)<br>• `negative_band`: per-band bool (True where P ≤ 0)<br>• `surface_pressure_intensity_index` (FpI)<br>• `negative_partial_power_index` (F+/-)<br>• `repeatability`, `dynamic_capability_index` (Ld)<br>• `achieved_grade`<br>• `surface_area`, `sound_power_level_a`, `grade` | `ir.sound_power_level, ir.achieved_grade` |
| `absorption_area` | `function` | **Equivalent absorption area (ISO 354 Eq. 5/7).**<br>• `t60`: T [s]<br>• `volume` V [m³]<br>• `temperature` [°C] (Default: 20)<br>• `speed_of_sound` [m/s] (overrides temperature)<br>• `m`: air attenuation [1/m] (Default: 0) | `A = absorption_area(t60, volume=200)`<br><br>• A [m²] |
| `absorption_coefficient` | `function` | **Sound absorption coefficient (ISO 354 Eq. 9).**<br>• `t1`, `t2`: empty / with-specimen T [s]<br>• `volume` V [m³]<br>• `sample_area` S [m²]<br>• `temperature1`/`temperature2` [°C]<br>• `speed_of_sound1`/`2`, `m1`/`m2` | `a = absorption_coefficient(t1, t2, 200, 10.8)`<br><br>• α_s (unclamped, may exceed 1) |
| `attenuation_from_alpha` | `function` | **ISO 9613-1 α → m (ISO 354 8.1.2.1).**<br>• `alpha`: attenuation [dB/m] | `m = attenuation_from_alpha(0.01)`<br><br>• m = α/(10 lg e) [1/m] |
| `air_attenuation` | `function` | **Atmospheric attenuation coefficient α (ISO 9613-1 Eq. 5).**<br>• `frequencies` [Hz]<br>• `temperature` [°C] (Default: 20)<br>• `relative_humidity` [%] (Default: 50)<br>• `pressure` [kPa] (Default: 101.325)<br>• `exact_midband`: snap to Table 1 midbands (Default: False) | `a = air_attenuation([1000, 4000], 20, 50)`<br><br>• α [dB/m] (×1000 = dB/km); out-of-range warns |
| `air_attenuation_m` | `function` | **ISO 354 power attenuation m from conditions (ISO 9613-1 + ISO 354).**<br>• Same parameters as `air_attenuation` | `m = air_attenuation_m([1000, 4000], 20, 50)`<br><br>• m = α/(10 lg e) [1/m] |
| `AtmosphericAbsorptionWarning` | `warning class` | **ISO 9613-1 out-of-range advisory.**<br>Emitted by `air_attenuation` when temperature/humidity/frequency leave the tabulated ranges or pressure exceeds 200 kPa; the result still returns | `warnings.simplefilter('error', AtmosphericAbsorptionWarning)` |
| `geometric_divergence` | `function` | **Geometrical divergence Adiv (ISO 9613-2 Eq. 7).**<br>• `distance` d [m] | `a = geometric_divergence(100.0)`<br><br>• 20 lg(d/d₀) + 11 = 51 dB at 100 m |
| `atmospheric_absorption` | `function` | **Atmospheric absorption term Aatm (ISO 9613-2 Eq. 8).**<br>• `distance` d [m]<br>• `frequencies` [Hz]<br>• `temperature`/`humidity`/`pressure` | `aatm = atmospheric_absorption(200, bands)`<br><br>• α·d per band [dB] |
| `ground_attenuation` | `function` | **Ground effect Agr, general method (ISO 9613-2 7.3.1, Eq. 9).**<br>• `distance` d, `source_height` hs, `receiver_height` hr [m]<br>• `frequencies` [Hz]<br>• `ground_source`/`ground_middle`/`ground_receiver` G ∈ [0,1]<br>• `projected_distance` dp [m] | `agr = ground_attenuation(200, 2, 2, bands, 1, 1, 1)`<br><br>• As+Ar+Am per band [dB] (negative = gain) |
| `ground_attenuation_alternative` | `function` | **Ground effect Agr, A-weighted method (ISO 9613-2 7.3.2, Eq. 10).**<br>• `distance` d [m]<br>• `mean_height` hm [m] | `agr = ground_attenuation_alternative(200, 2)`<br><br>• 4.8 − (2hm/d)·(17+300/d) ≥ 0 [dB] |
| `directivity_omega` | `function` | **Solid-angle directivity index DΩ (ISO 9613-2 Eq. 11).**<br>• `source_height` hs, `receiver_height` hr, `projected_distance` dp [m] | `dw = directivity_omega(1.5, 1.5, 200)`<br><br>• 0…~3 dB (add to Dc for the 7.3.2 method) |
| `Barrier` | `dataclass` | **Barrier diffraction geometry (ISO 9613-2 7.4).**<br>• `source_to_edge` dss, `edge_to_receiver` dsr [m]<br>• `parallel_distance` a [m] (Default: 0)<br>• `edge_separation` e [m] (Default: None → single diffraction)<br>• `ground_reflections_by_image` (Default: False → C₂=20)<br>• `lateral` (Default: False → top-edge) | `b = Barrier(source_to_edge=101, edge_to_receiver=101)`<br><br>• `.is_double` when e is given |
| `barrier_attenuation` | `function` | **Barrier diffraction Dz (ISO 9613-2 Eq. 14).**<br>• `barrier`: `Barrier`<br>• `distance` d [m]<br>• `frequencies` [Hz] | `dz = barrier_attenuation(b, 200, bands)`<br><br>• 10 lg[3+(C₂/λ)C₃ z Kmet], capped 20/25 dB |
| `meteorological_correction` | `function` | **Meteorological correction Cmet (ISO 9613-2 Eq. 21/22).**<br>• `projected_distance` dp, `source_height` hs, `receiver_height` hr [m]<br>• `c0`: factor C₀ [dB] | `c = meteorological_correction(200, 1.5, 1.5, 2.0)`<br><br>• C₀[1 − 10(hs+hr)/dp] ≥ 0 [dB] |
| `outdoor_propagation_attenuation` | `function` | **Total octave-band attenuation A (ISO 9613-2 Eq. 4).**<br>• `distance` d, `source_height` hs, `receiver_height` hr [m]<br>• `frequencies` [Hz]<br>• `ground_source`/`ground_middle`/`ground_receiver` G<br>• `barrier`: `Barrier` or None<br>• `temperature`/`humidity`/`pressure` (Default: 20 °C/70 %/101.325 kPa, a Table 2 reference atmosphere)<br>• `projected_distance` dp [m] | `att = outdoor_propagation_attenuation(200, 2, 2, bands, 1, 1, 1)`<br><br>• `OutdoorAttenuation` term breakdown |
| `predicted_receiver_level` | `function` | **Predicted octave-band receiver level (ISO 9613-2 Eq. 3/6).**<br>• `sound_power_level` Lw [dB]<br>• same geometry/ground/barrier/atmosphere params as `outdoor_propagation_attenuation`<br>• `directivity_index` Di, `d_omega` DΩ [dB]<br>• `c0`: subtract Cmet (Default: None) | `lp = predicted_receiver_level(lw, 200, 2, 2, bands)`<br><br>• LfT(DW) = Lw + Dc − A per band [dB] |
| `OutdoorAttenuation` | `dataclass` | **Per-band ISO 9613-2 attenuation breakdown.**<br>• `frequencies` [Hz]<br>• `a_div`, `a_atm`, `a_gr`, `a_bar` [dB]<br>• `a_total` = Adiv+Aatm+Agr+Abar [dB]<br>• `d_omega` [dB] | `att.a_div, att.a_bar, att.a_total` |
| `DEFAULT_FREQUENCIES` | `tuple` | **ISO 9613-2 nominal octave bands.**<br>(no parameters) | `DEFAULT_FREQUENCIES  # (63, …, 8000)` |
| `task_based_exposure` | `function` | **Task-based daily exposure LEX,8h + U (ISO 9612 Clause 9).**<br>• `tasks`: sequence of `Task`<br>• `instrument`: 'class1'/'class2'/'personal_exposimeter' (Default)<br>• `u3` [dB] (Default: 1.0)<br>• `include_duration_uncertainty` (Default: True)<br>• `warn` (Default: True) | `res = task_based_exposure(tasks)`<br><br>• `ExposureResult` with per-task breakdown |
| `job_based_exposure` | `function` | **Job-based daily exposure LEX,8h + U (ISO 9612 Clause 10).**<br>• `samples` Lp,A,eqT [dB]<br>• `effective_duration_hours` Te [h]<br>• `instrument`, `u3`<br>• `n_workers`/`sample_duration_hours`: Table 1 check | `res = job_based_exposure(samples, 7.5)`<br><br>• `ExposureResult` (Eq C.9 / Table C.4 budget) |
| `full_day_exposure` | `function` | **Full-day daily exposure LEX,8h + U (ISO 9612 Clause 11).**<br>• `samples` whole-day Lp,A,eqT [dB]<br>• `effective_duration_hours` Te [h]<br>• `instrument`, `u3`, `warn` | `res = full_day_exposure(samples, 9.25)`<br><br>• `ExposureResult`; 3 samples spanning ≥3 dB advise |
| `Task` | `dataclass` | **One task of a task-based measurement (ISO 9612 Clause 9).**<br>• `samples` [dB], `duration_hours` [h]<br>• `duration_samples`/`duration_range` (for u1b)<br>• `label`, `instrument` | `Task(samples=(80.1, 82.2), duration_hours=5.0)` |
| `ExposureResult` | `dataclass` | **Daily exposure and uncertainty (ISO 9612).**<br>• `lex_8h` [dB]<br>• `combined_standard_uncertainty` u [dB]<br>• `expanded_uncertainty` U = 1.65 u [dB]<br>• `upper_limit` = LEX,8h + U [dB]<br>• `strategy`, `sampling_advisory`, `tasks` | `res.lex_8h, res.upper_limit` |
| `TaskContribution` | `dataclass` | **Per-task breakdown inside `ExposureResult.tasks` (ISO 9612 Clause 9).**<br>• `label`, `lp_aeqt` (Eq. 7), `duration_hours`<br>• `lex_8h_contribution` (Eq. 8) [dB]<br>• uncertainty terms `u1a`, `u1b`, `c1a`, `c1b`, `u2`, `u3` | `res.tasks[0].lex_8h_contribution` |
| `table_c4_contribution` | `function` | **Sampling contribution c₁u₁ [dB] from Table C.4 (ISO 9612 job/full-day).**<br>• `n_samples`: N (clamped to [3, 30])<br>• `u1`: sampling standard uncertainty [dB]<br>• bilinear interpolation, anchored at u₁ = 0 | `table_c4_contribution(6, 2.0)  # 1.4` |
| `minimum_cumulative_duration_hours` | `function` | **Minimum cumulative measurement duration [h] (ISO 9612 Table 1).**<br>• `n_workers`: group size n_G (> 40 → 17 h; the standard advises splitting the group) | `minimum_cumulative_duration_hours(18)  # 10.75` |
| `COVERAGE_FACTOR` | `float` | **ISO 9612 coverage factor k = 1.65 (Clause 14).**<br>One-sided 95 % confidence: U = 1.65 u, upper limit LEX,8h + U | `COVERAGE_FACTOR  # 1.65` |
| `INSTRUMENT_U2` | `mapping` | **Instrument standard uncertainty u2 [dB] (ISO 9612 Table C.5).**<br>Keyed by `'class1'` (0.7), `'class2'` (1.5), `'personal_exposimeter'` (1.5) | `INSTRUMENT_U2['class1']  # 0.7` |
| `OccupationalExposureWarning` | `warning class` | **ISO 9612 sampling advisory.**<br>Emitted for the 3 dB task spread (Clause 9.3), c₁u₁ > 3.5 dB (Clause 10.4) or a short Table 1 cumulative duration | `warnings.simplefilter('error', OccupationalExposureWarning)` |
| `SoundPowerWarning` | `warning class` | **ISO 3744/3746/3741/9614-2 qualification issue.**<br>Emitted when the background margin is below the criterion, K2 exceeds the validity limit, a band's power is negative, or the room fails qualification; levels are then upper bounds | `warnings.simplefilter('error', SoundPowerWarning)` |
| `AbsorptionWarning` | `warning class` | **ISO 354 advisory.**<br>Emitted for a room below 150 m³, a sample area outside 10-12 m², an out-of-range temperature, or a non-physical α_s ≤ 0; the result still returns | `warnings.simplefilter('error', AbsorptionWarning)` |
| `speech_intelligibility_index` | `function` | **Speech Intelligibility Index (ANSI S3.5-1997, one-third-octave method).**<br>• `speech_spectrum`: 18 equivalent speech spectrum levels, 160 Hz–8 kHz [dB SPL], or a vocal-effort name 'normal'/'raised'/'loud'/'shout' (Table 3)<br>• `noise_spectrum`: equivalent noise spectrum levels [dB SPL] (Default: None → quiet, −80 dB)<br>• `threshold`: equivalent hearing threshold [dB HL] (Default: None → 0) | `res = speech_intelligibility_index("normal", noise_spectrum=[40.0]*18)`<br><br>• `SIIResult`; `res.sii` = 0.066 |
| `standard_speech_spectrum` | `function` | **Standard speech spectrum level by vocal effort (ANSI S3.5-1997 Table 3).**<br>• `vocal_effort`: 'normal', 'raised', 'loud' or 'shout' (Default: 'normal') | `u = standard_speech_spectrum('raised')`<br><br>• 18 band levels [dB SPL] |
| `SIIResult` | `dataclass` | **SII result.**<br>• `sii`: index in [0, 1]<br>• `band_audibility`: Ai per band (§5.8)<br>• `band_importance`: Ii (Table 3)<br>• `frequencies` [Hz]<br>• `speech_spectrum` / `disturbance` / `masking`: Ei′ / Di / Zi per band [dB]<br>• `.plot()` | `res.sii, res.band_audibility` |
| `noise_criterion` | `function` | **NC rating, tangency method (ANSI/ASA S12.2-2019).**<br>• `levels`: octave-band SPL [dB] (the 10 bands 16 Hz–8 kHz without `frequencies`)<br>• `frequencies`: optional band centres [Hz] (subset allowed) | `nc = noise_criterion(levels)`<br><br>• `NCResult`; highest NC curve touched |
| `room_criterion` | `function` | **RC Mark II rating (ANSI/ASA S12.2-2019 Annex D).**<br>• `levels`: octave-band SPL [dB]<br>• `frequencies`: optional band centres [Hz] | `rc = room_criterion(levels)`<br><br>• `RCResult`; LMF average + 'N'/'R'/'H'/'RH' tag |
| `nc_curve` | `function` | **NC curve levels (Table 1).**<br>• `index`: NC designation 15–70 (intermediate values interpolated band by band) | `nc_curve(35)  # [82, 71, 60, ...]`<br><br>• 10 band levels [dB], 16 Hz–8 kHz |
| `rc_curve` | `function` | **RC Mark II curve (Table D.1).**<br>• `index`: RC designation (value at 1000 Hz) | `rc_curve(35)`<br><br>• −5 dB/octave line, 10 bands [dB] |
| `NCResult` | `dataclass` | **NC rating result.**<br>• `rating`: NC value<br>• `governing_frequency`: band of the touch [Hz]<br>• `frequencies` [Hz], `levels` [dB]<br>• `.plot()` | `nc.rating, nc.governing_frequency` |
| `RCResult` | `dataclass` | **RC Mark II result.**<br>• `rating`: LMF rounded [dB], int<br>• `lmf`: 500/1000/2000 Hz average [dB]<br>• `classification`: 'N'/'R'/'H'/'RH'<br>• `reference_curve` [dB], `frequencies` [Hz], `levels` [dB]<br>• `.plot()` | `rc.rating, rc.classification` |
| `age_threshold` | `function` | **Age-related hearing threshold distribution (ISO 7029:2017).**<br>• `age`: years (≥ 18)<br>• `sex`: 'male'/'female' (Default: 'male')<br>• `fractile`: population fractile in (0, 1) (Default: 0.5)<br>• `frequencies`: subset of the 11 audiometric frequencies [Hz] (Default: None → 125–8000 Hz) | `at = age_threshold(60, 'male')`<br><br>• `AgeThresholdResult`; median at 4 kHz = 20.2 dB |
| `reference_threshold` | `function` | **Reference threshold of hearing, 0 dB HL (ISO 389-7:2006 Table 1).**<br>• `field`: 'free-field' or 'diffuse-field' (Default: 'free-field')<br>• `frequencies`: optional subset [Hz] | `t = reference_threshold()`<br><br>• dB SPL per audiometric frequency (1 kHz → 2.4) |
| `AgeThresholdResult` | `dataclass` | **Age threshold distribution.**<br>• `age`, `sex`, `fractile`<br>• `frequencies` [Hz]<br>• `median`: deviation from age 18 [dB]<br>• `spread_upper` / `spread_lower`: half-Gaussian su/sl [dB]<br>• `threshold`: value at `fractile` [dB]<br>• `.plot()` | `at.median, at.threshold` |
| `nipts` | `function` | **Noise-induced permanent threshold shift (ISO 1999:2013 §6.3).**<br>• `l_ex`: LEX,8h [dB]<br>• `years`: exposure duration (10–40 established; 1–10 extrapolated by Formula 3)<br>• `fractile`: (0, 1) (Default: 0.5)<br>• `frequencies`: subset [Hz] (Default: None → 500–6000 Hz) | `n = nipts(95.0, 20.0)`<br><br>• `NiptsResult`; N50 at 4 kHz = 23.0 dB |
| `htlan` | `function` | **Threshold associated with age and noise, H′ = H + N − HN/120 (ISO 1999 Formula 1).**<br>• `age`: years (≥ 18), `sex`: 'male'/'female'<br>• `l_ex`: LEX,8h [dB], `years`<br>• `fractile`: (0, 1) applied to both components (Default: 0.5)<br>• `frequencies` | `h = htlan(60, 'male', 95.0, 20.0)`<br><br>• `HtlanResult`; H′ at 4 kHz = 39.3 dB |
| `NiptsResult` | `dataclass` | **NIPTS distribution.**<br>• `l_ex`, `years`, `fractile`<br>• `frequencies` [Hz]<br>• `median`: N50 (Formula 2/3) [dB]<br>• `value`: NIPTS at `fractile` (Formula 4/5) [dB]<br>• `spread_upper` / `spread_lower`: du/dl [dB]<br>• `.plot()` | `n.median, n.value` |
| `HtlanResult` | `dataclass` | **Combined HTLAN result.**<br>• `age`, `sex`, `l_ex`, `years`, `fractile`<br>• `frequencies` [Hz]<br>• `htla`: age component H [dB]<br>• `nipts`: noise component N [dB]<br>• `threshold`: combined H′ [dB]<br>• `.plot()` | `h.htla, h.nipts, h.threshold` |
| `predicted_prominence` | `function` | **Predicted prominence P of an impulse (NT ACOU 112 Formula 1).**<br>• `onset_rate`: slope of the A/F level onset [dB/s] (> 0; qualifies above 10 dB/s)<br>• `level_difference`: level rise over the onset [dB] (> 0) | `predicted_prominence(50.0, 20.0)  # 7.7`<br><br>• P = 3 lg(rate) + 2 lg(diff) |
| `impulse_adjustment` | `function` | **LAeq adjustment KI (Formula 2).**<br>• `prominence`: P | `impulse_adjustment(7.7)  # 4.86`<br><br>• 1.8(P − 5) dB for P > 5, else 0 |
| `impulse_prominence` | `function` | **Governing prominence and adjustment of a set of impulses (clauses 7–8).**<br>• `onset_rates` [dB/s]<br>• `level_differences` [dB] | `r = impulse_prominence([50, 120], [20, 15])`<br><br>• `ImpulseProminenceResult` (P = 8.59, KI = 6.46 dB) |
| `rating_level` | `function` | **Rating level LAr,T over a reference time (clause 8 Note 1).**<br>• `laeq`: LAeq,N per sub-interval [dB]<br>• `adjustment`: KI,N per sub-interval [dB]<br>• `durations`, `reference_time`: same time unit | `rating_level([55, 60], [0, 4.9], [20, 10], 30)  # 60.9` |
| `ImpulseProminenceResult` | `dataclass` | **Impulse-prominence verdict.**<br>• `onset_rates` [dB/s], `level_differences` [dB]<br>• `per_impulse`: P of each impulse<br>• `prominence`: governing (highest) P<br>• `adjustment`: KI of the governing impulse [dB]<br>• `.plot()` | `r.prominence, r.adjustment` |
| `multiple_shock_assessment` | `function` | **Full multiple-shock assessment from seat acceleration (ISO 2631-5:2018).**<br>• `acceleration`: vertical seat az(t) [m/s²], `fs` [Hz]<br>• `start_age`: years, `years`: exposure years, `days_per_year`<br>• `exposure_time` / `measurement_time`: scale Dz to a daily dose (Default: None)<br>• `sex`: 'male'/'female' (Default: 'male')<br>• `mz`: MPa per m/s² (Default: sex-specific) | `res = multiple_shock_assessment(az, fs, start_age=25, years=30, days_per_year=220)`<br><br>• `MultipleShockResult` |
| `seat_to_spine_transfer` | `function` | **Seat-to-spine transfer function H(ω) (clause 5.2 Formula 1).**<br>• `frequencies` [Hz] | `H = seat_to_spine_transfer(freqs)`<br><br>• Complex response; unity at 0 Hz |
| `spinal_response` | `function` | **Vertical spinal response Az(t) (Formula 2).**<br>• `acceleration`: seat az(t) [m/s²]<br>• `fs` [Hz] | `Az = spinal_response(az, fs)`<br><br>• Same length as the input [m/s²] |
| `response_peaks` | `function` | **Positive response peaks Az,i (clause 5.3).**<br>• `response`: Az(t) | `peaks = response_peaks(Az)`<br><br>• Maxima between zero crossings [m/s²] |
| `dose_from_peaks` | `function` | **Acceleration dose Dz from peaks (Formula 3).**<br>• `peaks`: Az,i [m/s²] | `dz = dose_from_peaks(peaks)`<br><br>• Dz = 1.07 (Σ Az,i⁶)^(1/6) [m/s²] |
| `acceleration_dose` | `function` | **Acceleration dose Dz from a time history (Formulas 2 + 3).**<br>• `acceleration`: seat az(t) [m/s²], `fs` [Hz] | `dz = acceleration_dose(az, fs)`<br><br>• Dz [m/s²] |
| `daily_dose` | `function` | **Daily dose Dzd (Formula 4).**<br>• `dose`: Dz [m/s²]<br>• `exposure_time` td / `measurement_time` tm: same unit | `daily_dose(4.0, 8.0, 2.0)  # 5.04`<br><br>• Dz (td/tm)^(1/6) [m/s²] |
| `daily_dose_multi` | `function` | **Daily dose from several exposure conditions (Formula 5).**<br>• `doses`: Dz,j [m/s²]<br>• `exposure_times` / `measurement_times`: per condition | `dzd = daily_dose_multi(dz, td, tm)`<br><br>• [Σ Dz,j⁶ (td,j/tm,j)]^(1/6) [m/s²] |
| `compression_dose` | `function` | **Daily compressive stress Sd (Annex C Formula C.1).**<br>• `daily_dose_value`: Dzd [m/s²]<br>• `mz`: MPa per m/s² (Default: 0.029, 82 kg male) | `compression_dose(5.0)  # 0.145`<br><br>• Sd = mz·Dzd [MPa] |
| `static_stress` | `function` | **Static compressive stress Sstat = mz·9.81 (Annex C).**<br>• `mz` (Default: 0.029) | `static_stress()  # 0.284`<br><br>• [MPa] |
| `ultimate_strength` | `function` | **Ultimate lumbar strength Su at an age (Formula C.4).**<br>• `age`: years<br>• `sex`: 'male'/'female' (Default: 'male') | `ultimate_strength(45.0)  # 4.41`<br><br>• 6.75 − Sage·age [MPa] |
| `injury_risk` | `function` | **Cumulative injury stress variable R (Formula C.3).**<br>• `daily_compression`: Sd [MPa]<br>• `start_age`, `years`, `days_per_year`<br>• `sex`, `mz` | `R = injury_risk(0.5, start_age=25, years=30, days_per_year=220)  # 0.509` |
| `injury_probability` | `function` | **Probability of lumbar injury P(R) (Formula C.5, Weibull).**<br>• `risk`: R<br>• `sex` (Default: 'male') | `injury_probability(0.509)  # 0.0389`<br><br>• 1 − exp(−(R/α)^β) in 0–1 |
| `MultipleShockResult` | `dataclass` | **Multiple-shock health assessment.**<br>• `acceleration_dose` Dz, `daily_dose` Dzd [m/s²]<br>• `compression_dose` Sd [MPa]<br>• `risk` R, `probability` P(R)<br>• `sex`, `start_age`, `years`, `days_per_year`<br>• `peaks` [m/s²], `risk_thresholds`: R at 10/50/90 % (Table C.2)<br>• `.plot()` | `res.risk, res.probability` |
| `object_fraction` | `function` | **Object fraction ψ of an enclosed space (EN 12354-6 Formula 3).**<br>• `object_volumes` [m³]<br>• `volume`: empty space V [m³] | `object_fraction([12.0, 8.0], 500.0)  # 0.04` |
| `hard_object_absorption` | `function` | **Equivalent absorption area of a hard object (Formula 4).**<br>• `object_volume`: Vobj [m³] | `hard_object_absorption(8.0)  # 4.0`<br><br>• Aobj = Vobj^(2/3) [m²] |
| `air_absorption_area` | `function` | **Equivalent absorption area of the air (Formula 2).**<br>• `m`: power attenuation of air [Np/m]<br>• `volume` V [m³]<br>• `object_fraction` ψ (Default: 0.0) | `air_absorption_area(0.001, 500.0)  # 2.0`<br><br>• Aair = 4mV(1 − ψ) [m²] |
| `equivalent_absorption_area` | `function` | **Total equivalent sound absorption area (Formula 1).**<br>• `surfaces`: sequence of (area, absorption_coefficient) pairs (coefficient scalar or per band)<br>• `objects`: object areas Aobj [m²] (Default: ())<br>• `air_area`: Aair [m²] (Default: 0.0) | `A = equivalent_absorption_area([(100.0, 0.03), (50.0, 0.6)], objects=[4.0], air_area=2.0)  # 39.0` |
| `reverberation_time` | `function` | **Reverberation time from the absorption area (Formula 5).**<br>• `absorption_area` A [m²]<br>• `volume` V [m³]<br>• `object_fraction` ψ (Default: 0.0)<br>• `speed_of_sound` c0 [m/s] (Default: 345.6 → factor 0.16) | `reverberation_time(39.0, 500.0)  # 2.05`<br><br>• T = 55.3/c0 · V(1 − ψ)/A [s] |
| `enclosed_space_reverberation` | `function` | **Predicted A and T per octave band (EN 12354-6 Clause 4).**<br>• `surfaces`: (area, per-band α) pairs<br>• `volume` V [m³]<br>• `objects` [m²], `object_fraction` ψ<br>• `air_condition`: air-attenuation key, e.g. '20C_50-70' (Default: None → neglect air)<br>• `frequencies` [Hz] (Default: 125–8000 Hz octaves)<br>• `speed_of_sound` [m/s] | `res = enclosed_space_reverberation(surfaces, 500.0, air_condition="20C_50-70")`<br><br>• `ReverberationResult` |
| `ReverberationResult` | `dataclass` | **Enclosed-space absorption result.**<br>• `frequencies` [Hz]<br>• `absorption_area`: A per band [m²]<br>• `reverberation_time`: T per band [s]<br>• `volume` [m³], `object_fraction`<br>• `.plot()` | `res.absorption_area, res.reverberation_time` |
| `combine_uncertainty` | `function` | **GUM law of propagation of uncertainty (ISO/IEC Guide 98-3 clause 5).**<br>• `model`: measurement function f(x1…xN)<br>• `quantities`: input `Quantity` objects, in argument order<br>• `correlation`: optional N×N matrix r_ij (Default: None → uncorrelated) | `u = combine_uncertainty(lambda a, b: a*b, [Quantity(10.0, 0.1), Quantity(5.0, 0.2)])`<br><br>• `UncertaintyResult`; uc = 2.062 |
| `monte_carlo` | `function` | **Monte Carlo propagation (Guide 98-3-1, Supplement 1).**<br>• `model`: vectorised f(x1…xN)<br>• `quantities`: input `Quantity` objects<br>• `trials`: M (Default: 1000000)<br>• `coverage`: interval probability (Default: 0.95)<br>• `seed`: reproducibility (Default: None) | `mc = monte_carlo(model, quantities, seed=1)`<br><br>• `MonteCarloResult` (mean, u, coverage interval) |
| `rectangular` | `function` | **Type B quantity, rectangular PDF (GUM 4.3.7).**<br>• `value`, `half_width` a, `name` | `rectangular(20.0, 0.5)`<br><br>• `Quantity` with u = a/√3 = 0.289 |
| `triangular` | `function` | **Type B quantity, triangular PDF (GUM 4.3.9).**<br>• `value`, `half_width` a, `name` | `triangular(20.0, 0.5)`<br><br>• `Quantity` with u = a/√6 |
| `u_shaped` | `function` | **Type B quantity, U-shaped (arcsine) PDF.**<br>• `value`, `half_width` a, `name` | `u_shaped(20.0, 0.5)`<br><br>• `Quantity` with u = a/√2 |
| `Quantity` | `dataclass` | **Input quantity of a measurement model (GUM clause 4).**<br>• `value`: estimate xi<br>• `uncertainty`: u(xi) ≥ 0<br>• `distribution`: 'gaussian'/'rectangular'/'triangular'/'u-shaped' (Default: 'gaussian')<br>• `dof`: degrees of freedom (Default: inf)<br>• `name`: budget label | `Quantity(94.0, 0.3, name="calibrator")` |
| `UncertaintyResult` | `dataclass` | **GUM propagation result.**<br>• `value`: y = f(x1…xN)<br>• `combined_uncertainty`: uc(y)<br>• `sensitivities`: ci = ∂f/∂xi<br>• `contributions`: \|ci\|·u(xi)<br>• `effective_dof`: Welch–Satterthwaite<br>• `names`<br>• `.plot()`: uncertainty budget | `u.combined_uncertainty, u.contributions` |
| `MonteCarloResult` | `dataclass` | **Monte Carlo result.**<br>• `value`: sample mean<br>• `standard_uncertainty`: sample std<br>• `interval`: (low, high) coverage interval (§7.7)<br>• `coverage`, `trials` | `mc.value, mc.interval` |
| `sound_power_anechoic` | `function` | **Precision sound power in an (hemi-)anechoic room (ISO 3745:2012).**<br>• `levels_positions`: (NM, NB) position levels [dB]<br>• `surface`: 'sphere'/'hemisphere'<br>• `radius` r [m]<br>• `background_levels` + `frequencies`: for K1i<br>• `areas`: partial areas Si (Eq. 13) (Default: equal-area Eq. 12)<br>• `temperature` [°C] (Default: 23), `static_pressure` [kPa] (Default: 101.325)<br>• `air_absorption_coefficient`: α(f) [dB/m] for C3<br>• `sigma_omc` [dB] (Default: 0), `coverage_factor` k (Default: 2.0) | `res = sound_power_anechoic(levels, 'hemisphere', radius=2.0, frequencies=f)`<br><br>• `PrecisionSoundPowerResult` |
| `PrecisionSoundPowerResult` | `dataclass` | **ISO 3745 sound power result.**<br>• `sound_power_level` [dB], `sound_power_level_a` [dB]<br>• `surface_pressure_level`, `mean_pressure_level` [dB]<br>• `background_correction`: K1i (NM, NB) [dB]<br>• `c1`, `c2`, `c3`: meteorological corrections [dB]<br>• `directivity_index` DIi, `non_uniformity_index` VIr [dB]<br>• `surface_area` [m²], `surface`<br>• `uncertainty`, `uncertainty_bands`, `coverage_factor`<br>• `.plot()` | `res.sound_power_level, res.uncertainty` |
| `precision_positions` | `function` | **ISO 3745 microphone coordinates (Annex D/E).**<br>• `surface`: 'sphere' (Table D.1) / 'hemisphere' (Tables E.1/E.2)<br>• `radius` r [m]<br>• `array`: 'general'/'broadband' (Default: 'general')<br>• `count`: 20 or 40 (Default: 40) | `xyz = precision_positions('hemisphere', radius=2.0)`<br><br>• (40, 3) coordinates [m] |
| `precision_background_correction` | `function` | **Per-position background correction K1i (ISO 3745 Eq. 11).**<br>• `source_levels` / `background_levels`: (NM, NB) [dB]<br>• `frequencies` [Hz]: per-band criterion (10 dB for 250–5000 Hz, 6 dB outside) | `k1 = precision_background_correction(src, bg, f)`<br><br>• K1i [dB]; clamped + `SoundPowerWarning` below the criterion |
| `meteorological_corrections` | `function` | **Corrections C1, C2, C3 (ISO 3745 Eq. 14 block).**<br>• `temperature` θ [°C] (Default: 23), `static_pressure` ps [kPa] (Default: 101.325)<br>• `air_absorption_coefficient`: α(f) [dB/m] for C3 (Default: None → C3 = 0)<br>• `radius` r [m] (Default: 1.0) | `met = meteorological_corrections(23.0, 101.325)`<br><br>• `MeteorologicalCorrection`; C1 = −0.128 dB, C2 = 0 at reference |
| `MeteorologicalCorrection` | `dataclass` | **C1/C2/C3 corrections.**<br>• `c1`: reference-quantity correction [dB]<br>• `c2`: radiation-impedance correction [dB]<br>• `c3`: air-absorption correction [dB], scalar or per band | `met.c1, met.c2, met.c3` |
| `precision_uncertainty` | `function` | **Expanded uncertainty U = k·√(σR0² + σomc²) (ISO 3745 Eq. 24/25).**<br>• `sigma_r0`: reproducibility (Tables 2/3) [dB]<br>• `sigma_omc` [dB] (Default: 0.0)<br>• `coverage_factor` k (Default: 2.0; 1.6 one-sided) | `precision_uncertainty(0.5)  # 1.0`<br><br>• U [dB], scalar or per band |
| `sound_power_intensity_precision` | `function` | **Sound power by intensity scanning, precision (ISO 9614-3:2002).**<br>• `partial_intensity`: (N, NB) signed In,i [W/m²]<br>• `areas`: partial areas Si [m²]<br>• `frequencies` [Hz]: for LWA<br>• `temperature` [°C] (Default: 23), `barometric_pressure` [Pa] (Default: 101325): for LW0 (Eq. 10) | `res = sound_power_intensity_precision(In, areas, frequencies=f)`<br><br>• `PrecisionIntensityResult` |
| `PrecisionIntensityResult` | `dataclass` | **ISO 9614-3 scanning result.**<br>• `partial_power`: Pi = In,i·Si [W]<br>• `sound_power` P, `sound_power_level` LW [dB] (NaN where P ≤ 0)<br>• `sound_power_level_normalized`: LW0 [dB]<br>• `not_applicable_band`: per-band bool<br>• `surface_area` [m²], `sound_power_level_a` [dB]<br>• `.plot()` | `res.sound_power_level, res.not_applicable_band` |
| `precision_field_indicators` | `function` | **ISO 9614-3 Annex B field indicators.**<br>• `segment_intensity`: (N, NB) signed In,j [W/m²]<br>• `segment_pressure_levels`: (N, NB) Lpj [dB]<br>• `time_window_intensity`: (M, NB) for FT (Default: None) | `fi = precision_field_indicators(In, lp)`<br><br>• `PrecisionFieldIndicators` |
| `PrecisionFieldIndicators` | `dataclass` | **Annex B indicators (per band).**<br>• `ft`: temporal variability (= F1) or None<br>• `f_pi_unsigned`: F_pIn unsigned (= F2)<br>• `f_pi_signed`: F_pIn signed (= F3), ≥ unsigned<br>• `fs`: field non-uniformity FS (= F4) | `fi.f_pi_signed, fi.fs` |
| `precision_qualification` | `function` | **The five ISO 9614-3 Annex C acceptance criteria.**<br>• `indicators`: `PrecisionFieldIndicators`<br>• `scan_intensity_level_1`/`_2`: LIn per scan [dB] (criterion 1)<br>• `pressure_residual_index`: δpI0 [dB] (criterion 2, K = 10)<br>• `field_nonuniformity_1`/`_2`: FS per scan density (criterion 5)<br>• `frequencies` [Hz] or `repeatability_limit`: Table 1 limit s | `q = precision_qualification(fi, pressure_residual_index=18.0)`<br><br>• `PrecisionCriteria` |
| `PrecisionCriteria` | `dataclass` | **Annex C pass/fail per band.**<br>• `criterion_1`…`criterion_5`: bool arrays or None where not evaluable<br>• `qualified`: conjunction of criteria 1–4 or None | `q.qualified, q.criterion_2` |
| `plane_wave_frequency_range` | `function` | **Working plane-wave range (f_l, f_u) (ISO 10534-2 §4.2–4.5).**<br>• `spacing` s [m]<br>• `speed_of_sound` c0 [m/s]<br>• `diameter` d [m] (Default: None → spacing bound only)<br>• `shape`: 'circular'/'rectangular' (Default: 'circular') | `plane_wave_frequency_range(0.05, 343.2, diameter=0.1)  # (343.2, 1990.6)`<br><br>• [Hz] |
| `speed_of_sound_iso` | `function` | **Speed of sound (ISO 10534-2 Eq. 5).**<br>• `temperature` T [K] | `speed_of_sound_iso(293.0)  # 343.2`<br><br>• c0 = 343.2 √(T/293) [m/s] |
| `air_density_iso` | `function` | **Air density (ISO 10534-2 Eq. 7).**<br>• `temperature` T [K]<br>• `atmospheric_pressure` [kPa] (Default: 101.325) | `air_density_iso(293.0)  # 1.186`<br><br>• ρ [kg/m³] |
| `speed_of_sound_astm` | `function` | **Speed of sound (ASTM E2611-19 Eq. 4).**<br>• `temperature` T [°C] | `speed_of_sound_astm(20.0)  # 343.2`<br><br>• 20.047 √(273.15 + T) [m/s] |
| `air_density_astm` | `function` | **Air density (ASTM E2611-19 Eq. 5).**<br>• `temperature` T [°C]<br>• `atmospheric_pressure` P [kPa] (Default: 101.325) | `air_density_astm(20.0)  # 1.202`<br><br>• ρ [kg/m³] |
| `characteristic_impedance` | `function` | **Characteristic impedance of air ρc.**<br>• `density` ρ [kg/m³]<br>• `speed_of_sound` c [m/s] | `characteristic_impedance(1.186, 343.2)  # 407.0`<br><br>• [rayl] |
| `tube_attenuation_constant` | `function` | **Lower-bound tube attenuation k0″ (ISO 10534-2 Eq. A.18).**<br>• `frequency` f [Hz]<br>• `speed_of_sound` c0 [m/s]<br>• `diameter` d [m] (hydraulic for rectangular) | `tube_attenuation_constant(1000.0, 343.2, 0.1)  # 0.0179`<br><br>• [Np/m] |
| `tube_wavenumber` | `function` | **Complex wavenumber k0 = k0′ − j k0″ (ISO 10534-2 §2.6).**<br>• `frequency` f [Hz]<br>• `speed_of_sound` c0 [m/s]<br>• `attenuation`: k0″ [Np/m] (Default: None → lossless) | `tube_wavenumber(1000.0, 343.2, attenuation=0.018)`<br><br>• 18.308 − 0.018j [1/m] |
| `mic_calibration_factor` | `function` | **Microphone-mismatch calibration factor Hc (ISO 10534-2 Eq. 10).**<br>• `h12_config1`: H12 in the standard configuration<br>• `h12_config2`: H12 with the microphones interchanged | `hc = mic_calibration_factor(h12_a, h12_b)`<br><br>• Hc = √(H12ᴵ/H12ᴵᴵ) (complex) |
| `apply_mic_calibration` | `function` | **Apply the calibration factor (Eq. 13).**<br>• `h12_uncorrected`<br>• `calibration_factor`: Hc | `h12 = apply_mic_calibration(h12_raw, hc)`<br><br>• H12 = H12,raw/Hc |
| `reflection_factor` | `function` | **Complex reflection factor at the sample surface (ISO 10534-2 Eq. 17).**<br>• `h12`: corrected transfer function<br>• `spacing` s [m]<br>• `x1`: sample to the farther microphone [m]<br>• `wavenumber`: complex k0 | `r = reflection_factor(h12, spacing=0.05, x1=0.15, wavenumber=k0)`<br><br>• r = (H12 − HI)/(HR − H12)·e^(+2jk0x1) |
| `absorption_from_reflection` | `function` | **Normal-incidence absorption coefficient (Eq. 18).**<br>• `reflection`: complex r | `absorption_from_reflection(0.5)  # 0.75`<br><br>• α = 1 − \|r\|² |
| `surface_impedance` | `function` | **Absolute surface impedance Z (Eq. 19).**<br>• `reflection`: complex r<br>• `characteristic_impedance`: ρc0 [rayl] | `surface_impedance(0.5, 407.0)  # 1221`<br><br>• Z = ρc0(1 + r)/(1 − r) [rayl] |
| `normalized_surface_impedance` | `function` | **Normalised surface impedance Z/(ρc0) (Eq. 19).**<br>• `reflection`: complex r | `normalized_surface_impedance(0.5)  # 3.0` |
| `normalized_surface_admittance` | `function` | **Normalised surface admittance Gρc0 (Eq. 20).**<br>• `reflection`: complex r | `normalized_surface_admittance(0.5)  # 0.333`<br><br>• (1 − r)/(1 + r) |
| `two_microphone_impedance` | `function` | **Full two-microphone reduction (ISO 10534-2 Clause 7).**<br>• `h12`: corrected transfer function<br>• `frequency` f [Hz]<br>• `spacing` s [m], `x1` [m]<br>• `speed_of_sound` c0 [m/s], `characteristic_impedance` ρc0 [rayl]<br>• `attenuation`: k0″ [Np/m] (Default: None)<br>• `diameter` + `shape`: activate the plane-wave range check | `res = two_microphone_impedance(h12, frequency=f, spacing=0.05, x1=0.15, speed_of_sound=343.2, characteristic_impedance=407.0)`<br><br>• `ImpedanceTubeResult` |
| `ImpedanceTubeResult` | `dataclass` | **Two-microphone result per frequency.**<br>• `frequency` [Hz]<br>• `reflection`: complex r (Eq. 17)<br>• `surface_impedance` [rayl], `normalized_impedance` (Eq. 19)<br>• `absorption`: α = 1 − \|r\|² (Eq. 18) | `res.absorption, res.normalized_impedance` |
| `ImpedanceTubeWarning` | `warning class` | **ISO 10534-2 advisory.**<br>Emitted by `two_microphone_impedance` for frequencies outside the plane-wave working range (Eqs. 1–4); the results are still returned | `warnings.simplefilter('error', ImpedanceTubeWarning)` |
| `standing_wave_ratio_from_level` | `function` | **Standing-wave ratio from ΔL (ISO 10534-1 Eq. 15).**<br>• `level_difference`: Lmax − Lmin [dB] | `standing_wave_ratio_from_level(20.0)  # 10.0`<br><br>• s = 10^(ΔL/20) |
| `standing_wave_reflection_magnitude` | `function` | **Reflection magnitude from the SWR (Eq. 14).**<br>• `swr`: s ≥ 1 | `standing_wave_reflection_magnitude(10.0)  # 0.818`<br><br>• \|r\| = (s − 1)/(s + 1) |
| `standing_wave_reflection` | `function` | **Complex reflection factor from the standing wave (Eqs. 17–23).**<br>• `swr`: s<br>• `first_min_distance`: x_min1 [m]<br>• `wavelength`: λ0 [m] | `standing_wave_reflection(10.0, 0.05, 0.4)  # -0.818j`<br><br>• phase φ = π(4x_min1/λ0 − 1) |
| `standing_wave_absorption` | `function` | **Absorption from the SWR (Eqs. 9 + 14).**<br>• `swr`: s ≥ 1 | `standing_wave_absorption(10.0)  # 0.331`<br><br>• α = 4s/(s + 1)² |
| `standing_wave_normalized_impedance` | `function` | **Normalised impedance from the standing wave (Eqs. 24–26).**<br>• `swr`, `first_min_distance` [m], `wavelength` [m] | `standing_wave_normalized_impedance(10.0, 0.05, 0.4)`<br><br>• 0.198 − 0.98j |
| `wave_decomposition` | `function` | **Decompose the field into (A, B, C, D) (ASTM E2611-19 Eqs. 17–20).**<br>• `h1`…`h4`: microphone transfer functions<br>• `l1`, `s1`, `l2`, `s2`: geometry [m]<br>• `wavenumber` k | `A, B, C, D = wave_decomposition(h1, h2, h3, h4, l1=0.2, s1=0.05, l2=0.2, s2=0.05, wavenumber=k)`<br><br>• Forward/backward amplitudes, both sides |
| `face_quantities` | `function` | **Face pressures and velocities (Eq. 21).**<br>• `a`, `b`, `c`, `d`: wave amplitudes<br>• `wavenumber` k, `thickness` d [m], `characteristic_impedance` ρc | `p0, pd, u0, ud = face_quantities(A, B, C, D, wavenumber=k, thickness=0.05, characteristic_impedance=407.0)` |
| `transfer_matrix_two_load` | `function` | **Two-load transfer matrix (ASTM E2611-19 Eqs. 17–22).**<br>• `load_a`, `load_b`: (H1, H2, H3, H4) per termination<br>• `l1`, `s1`, `l2`, `s2`, `thickness` [m]<br>• `wavenumber`, `characteristic_impedance` | `T = transfer_matrix_two_load(load_a, load_b, l1=0.2, s1=0.05, l2=0.2, s2=0.05, thickness=0.05, wavenumber=k, characteristic_impedance=407.0)`<br><br>• `TransferMatrix` |
| `transfer_matrix_one_load` | `function` | **One-load transfer matrix, symmetric specimen (Eqs. 23–24).**<br>• `load`: (H1, H2, H3, H4)<br>• Same geometry parameters as `transfer_matrix_two_load` | `T = transfer_matrix_one_load(load, l1=0.2, s1=0.05, l2=0.2, s2=0.05, thickness=0.05, wavenumber=k, characteristic_impedance=407.0)`<br><br>• Requires reciprocity + symmetry |
| `air_layer_transfer_matrix` | `function` | **Analytic loss-free air-layer matrix (validation reference).**<br>• `wavenumber` k<br>• `thickness` d [m]<br>• `characteristic_impedance` ρc [rayl] | `T = air_layer_transfer_matrix(k, 0.05, 407.0)`<br><br>• det(T) = 1, T11 = T22 |
| `TransferMatrix` | `dataclass` | **Acoustic transfer matrix [[T11, T12], [T21, T22]] (ASTM E2611-19 Eq. 16).**<br>• `t11`, `t12`, `t21`, `t22`: complex, scalar or per frequency | `T.t11, T.t12` |
| `airflow_resistance` | `function` | **Airflow resistance R = Δp/qv (ISO 9053-1:2018 §3.1).**<br>• `pressure_drop` Δp [Pa]<br>• `volume_flow_rate` qv [m³/s] | `airflow_resistance(2.0, 0.0005)  # 4000.0`<br><br>• [Pa·s/m³] |
| `specific_airflow_resistance` | `function` | **Specific airflow resistance Rs (§3.2).**<br>• `resistance` R + `area` A, **or** `pressure_drop` Δp + `velocity` u | `specific_airflow_resistance(4000.0, 0.01)  # 40.0`<br><br>• Rs = R·A = Δp/u [Pa·s/m] |
| `airflow_resistivity` | `function` | **Airflow resistivity σ = Rs/d (§3.3).**<br>• `specific_resistance` Rs [Pa·s/m]<br>• `thickness` d [m] | `airflow_resistivity(40.0, 0.05)  # 800.0`<br><br>• [Pa·s/m²] |
| `linear_airflow_velocity` | `function` | **Linear airflow velocity u = qv/A (§3.4).**<br>• `volume_flow_rate` qv [m³/s]<br>• `area` A [m²] | `linear_airflow_velocity(5e-6, 0.01)  # 0.0005`<br><br>• [m/s] |
| `static_airflow_resistance` | `function` | **Stepwise static-method determination (ISO 9053-1 §7.5).**<br>• `velocities` u [m/s], `pressure_drops` Δp [Pa] (≥ 2 steps)<br>• `area` A [m²]<br>• `thickness` d [m] (Default: None → no σ)<br>• `evaluation_velocity` [m/s] (Default: 0.0005) | `res = static_airflow_resistance([0.0005, 0.001, 0.002], [0.02, 0.041, 0.086], 0.01, 0.05)`<br><br>• `StaticAirflowResult` (Rs = 40.0, σ = 800) |
| `StaticAirflowResult` | `dataclass` | **Static-method result at the evaluation velocity.**<br>• `resistance` R [Pa·s/m³], `specific_resistance` Rs [Pa·s/m]<br>• `resistivity` σ [Pa·s/m²] or None<br>• `evaluation_velocity` [m/s], `pressure_drop` [Pa]<br>• `linear_coefficient` a (zero-velocity Rs), `quadratic_coefficient` b | `res.specific_resistance, res.resistivity` |
| `piston_volume_flow_rate` | `function` | **RMS piston volume flow qv = 2πf·h·AP (ISO 9053-2 §6.2).**<br>• `frequency` f [Hz]<br>• `stroke_amplitude` h [m]<br>• `piston_area` AP [m²] | `piston_volume_flow_rate(2.0, 0.005, 0.01)  # 0.000628`<br><br>• [m³/s] |
| `alternating_airflow_resistance` | `function` | **Alternating-method resistance (ISO 9053-2:2020 Formula 2).**<br>• `level_specimen` Lps / `level_termination` Lpt [dB]<br>• `piston_stroke_specimen` hs / `piston_stroke_termination` ht [m]<br>• `frequency` f [Hz] (1–4 Hz), `cavity_volume` V [m³]<br>• `static_pressure` [Pa] (Default: 101325)<br>• `kappa_prime` κ′ (Default: 1.4; use `effective_kappa` for Annex A conformity)<br>• `background_level` Lpb [dB] (Default: None) | `r = alternating_airflow_resistance(78.0, 60.0, piston_stroke_specimen=5e-3, piston_stroke_termination=5e-4, frequency=2.0, cavity_volume=7.854e-4)`<br><br>• R [Pa·s/m³]; `AirflowResistanceWarning` when criteria fail |
| `thermal_boundary_layer_thickness` | `function` | **Thermal boundary-layer thickness b (ISO 9053-2 Formulas A.4/A.5).**<br>• `frequency` f [Hz]<br>• Air properties (Default: Annex A.3 values) | `thermal_boundary_layer_thickness(2.0)  # 0.00183`<br><br>• [m] |
| `effective_kappa` | `function` | **Effective ratio of specific heats κ′ (Formula A.7).**<br>• `cavity_surface` S [m²], `cavity_volume` V [m³]<br>• `frequency` f [Hz]<br>• Air properties (Default: Annex A.3 values) | `effective_kappa(0.0471, 7.854e-4, 2.0)  # 1.37`<br><br>• The Annex A.3 worked example |
| `AirflowResistanceWarning` | `warning class` | **ISO 9053 advisory.**<br>Emitted for a velocity above the 15 mm/s static limit, a piston frequency outside 1–4 Hz, or a failed Formula 3/4 validity criterion | `warnings.simplefilter('error', AirflowResistanceWarning)` |
| `practical_absorption_coefficient` | `function` | **Practical coefficients αp (ISO 11654 §4.1).**<br>• `third_octave_alpha_s`: 15 one-third-octave αs, 200–5000 Hz (sequence or mapping keyed by band) | `ap = practical_absorption_coefficient(alpha_s)`<br><br>• 5 octave values (250–4000 Hz), 0.05 steps, capped at 1.00 |
| `weighted_absorption` | `function` | **Weighted absorption αw + class (ISO 11654 §4.2).**<br>• `alpha_p`: the 5 octave practical coefficients | `w = weighted_absorption([0.25, 0.7, 0.95, 1.0, 0.85])`<br><br>• `AbsorptionRatingResult` (αw = 0.55, class D, 'MH') |
| `absorption_class` | `function` | **Sound absorption class (Table B.1).**<br>• `alpha_w`: multiple of 0.05 in [0, 1] | `absorption_class(0.7)  # 'C'`<br><br>• 'A'–'E' or 'Not classified' |
| `AbsorptionRatingResult` | `dataclass` | **αw rating result.**<br>• `alpha_w`: shifted curve read at 500 Hz<br>• `shape_indicator`: 'L'/'M'/'H' concatenation or ''<br>• `absorption_class`: 'A'–'E'/'Not classified'<br>• `shift`, `unfavourable_sum` (≤ 0.10)<br>• `band_centers` [Hz], `measured`, `shifted_reference`<br>• `.plot()` | `w.alpha_w, w.absorption_class` |
| `OCTAVE_BANDS` | `tuple` | **ISO 11654 octave rating bands [Hz].**<br>(250, 500, 1000, 2000, 4000) | `OCTAVE_BANDS  # (250, ..., 4000)` |
| `THIRD_OCTAVE_BANDS` | `tuple` | **ISO 11654 one-third-octave input bands [Hz].**<br>200 Hz to 5000 Hz (15 bands) | `THIRD_OCTAVE_BANDS[0]  # 200` |
| `REFERENCE_CURVE` | `mapping` | **ISO 11654 Figure 1 reference curve (read-only).**<br>Keyed by octave band [Hz] → coefficient | `REFERENCE_CURVE[250]  # 0.8` |
| `speed_of_sound` | `function` | **Speed of sound (ISO 17497-1 Eq. 2).**<br>• `temperature` t [°C] | `speed_of_sound(20.0)  # 343.2`<br><br>• 343.2 √((273.15 + t)/293.15) [m/s] |
| `air_attenuation_coefficient` | `function` | **Energy attenuation m from ISO 9613-1 α (ISO 17497-1 Eq. 3).**<br>• `pressure_attenuation_db_per_m`: α [dB/m] | `air_attenuation_coefficient(0.005)  # 0.00115`<br><br>• m ≈ α/4.343 [1/m] |
| `random_incidence_absorption` | `function` | **Random-incidence absorption αs (ISO 17497-1 Eq. 1).**<br>• `volume` V [m³], `area` S [m²]<br>• `c1`/`T1`: static base plate, no sample<br>• `c2`/`T2`: with the test sample<br>• `m1`/`m2`: air attenuation [1/m] (Default: 0) | `a_s = random_incidence_absorption(200.0, 10.8, c1=343.0, T1=2.5, c2=343.2, T2=1.8)  # 0.463` |
| `specular_absorption_coefficient` | `function` | **Specular absorption αspec (Eq. 4).**<br>• `volume`, `area`<br>• `c3`/`T3`: rotating base plate, no sample<br>• `c4`/`T4`: sample on the rotating turntable<br>• `m3`/`m4` (Default: 0) | `a_spec = specular_absorption_coefficient(200.0, 10.8, c3=c3, T3=t3, c4=c4, T4=t4)`<br><br>• Includes the energy lost to scattering |
| `scattering_coefficient` | `function` | **Random-incidence scattering coefficient s (Eq. 5).**<br>• `alpha_spec`, `alpha_s`<br>• `truncate_negative`: clip s < 0 to 0 (Default: True); s > 1 is kept | `scattering_coefficient(0.45, 0.30)  # 0.214`<br><br>• s = (αspec − αs)/(1 − αs) |
| `scattering_coefficient_spectrum` | `function` | **Scattering spectrum s(f) (Eq. 5).**<br>• `frequencies`: one-third-octave centres [Hz]<br>• `specular_absorption`, `random_absorption`: per band<br>• `truncate_negative` (Default: True) | `res = scattering_coefficient_spectrum(f, a_spec, a_s)`<br><br>• `ScatteringResult` |
| `ScatteringResult` | `dataclass` | **Scattering spectrum result.**<br>• `frequencies` [Hz]<br>• `scattering`: s per band<br>• `random_incidence`: αs, `specular`: αspec<br>• `.plot()` | `res.scattering` |
| `base_plate_scattering` | `function` | **Scattering of the base plate alone (Eq. 6).**<br>• `volume`, `area`<br>• `c1`/`T1`: static, `c3`/`T3`: rotating<br>• `m1`/`m3` (Default: 0) | `s_base = base_plate_scattering(200.0, 10.8, c1=c1, T1=t1, c3=c3, T3=t3)`<br><br>• Quality metric vs Table 1 |
| `check_base_plate_scattering` | `function` | **Verify the base plate against Table 1 (Clause 6.2).**<br>• `scattering`: mapping by band [Hz] or 18 values ordered as `BASE_PLATE_BANDS` | `check_base_plate_scattering(s_base)  # ()`<br><br>• Offending band centres; `ScatteringDiffusionWarning` if any |
| `BASE_PLATE_BANDS` | `tuple` | **ISO 17497-1 base-plate check bands [Hz].**<br>100 Hz to 5000 Hz (18 one-third octaves) | `BASE_PLATE_BANDS[0]  # 100` |
| `BASE_PLATE_MAX_SCATTERING` | `mapping` | **Table 1 base-plate scattering limits (read-only).**<br>Keyed by band [Hz] → maximum s | `BASE_PLATE_MAX_SCATTERING[500]  # 0.05` |
| `reverberation_time_uncertainty` | `function` | **Standard uncertainty of a mean T (ISO 17497-1 Eq. A.1).**<br>• `times`: N ≥ 2 spatially-averaged measurements [s] | `reverberation_time_uncertainty([2.31, 2.28, 2.35])  # 0.0203`<br><br>• Standard error of the mean [s] |
| `absorption_coefficient_uncertainty` | `function` | **Uncertainty of a Sabine coefficient (Eqs. A.3/A.4).**<br>• `volume`, `area`<br>• `c` [m/s]<br>• `T_a`/`u_a`, `T_b`/`u_b`: the two situations [s] | `u_alpha = absorption_coefficient_uncertainty(200.0, 10.8, c=343.2, T_a=2.5, u_a=0.02, T_b=1.8, u_b=0.02)` |
| `scattering_coefficient_uncertainty` | `function` | **Uncertainty of the scattering coefficient (Eq. A.5).**<br>• `alpha_spec`, `alpha_s`<br>• `u_alpha_spec`, `u_alpha_s` | `u = scattering_coefficient_uncertainty(0.45, 0.30, 0.02, 0.02)`<br><br>• `ScatteringUncertainty` (U = 2u, 95 %) |
| `ScatteringUncertainty` | `dataclass` | **Scattering uncertainty result.**<br>• `u_scattering`: combined standard u_s<br>• `expanded`: U = 2u_s | `u.u_scattering, u.expanded` |
| `directional_diffusion_coefficient` | `function` | **Directional diffusion coefficient d_θ (ISO 17497-2 Formulas 5/6).**<br>• `levels`: n ≥ 2 reflected SPL [dB] (−inf = zero energy)<br>• `area_weights`: Ni (Formula 8) (Default: None → equal-area Formula 5) | `directional_diffusion_coefficient([-10., -12., -15., -11., -13.])  # 0.854` |
| `directional_diffusion` | `function` | **Polar response + its coefficient.**<br>• `angles` [°], `levels` [dB]<br>• `weights`: Ni (Default: None) | `res = directional_diffusion(angles, levels)`<br><br>• `DiffusionResult` |
| `DiffusionResult` | `dataclass` | **Polar diffusion result.**<br>• `angles` [°], `levels` [dB]<br>• `coefficient`: d_θ (autocorrelation)<br>• `.plot()` | `res.coefficient` |
| `normalized_diffusion_coefficient` | `function` | **Normalised coefficient d_θ,n (Formula 7).**<br>• `d_theta`: test surface<br>• `d_theta_reference`: flat reference | `normalized_diffusion_coefficient(0.6, 0.2)  # 0.5`<br><br>• (d − d_r)/(1 − d_r) |
| `area_factors` | `function` | **Per-receiver area weights Ni (Clause 8.3 Formula 8).**<br>• `elevations`: θ [°], 0–90<br>• `delta_theta` [°]<br>• `delta_phi` [°] (Default: None → `delta_theta`) | `n_i = area_factors([0, 15, 30, 45, 60, 75, 90], delta_theta=15.0)`<br><br>• Dimensionless, min 1 |
| `random_incidence_diffusion` | `function` | **Random-incidence diffusion coefficient d (Clause 8.4).**<br>• `directional_coefficients`: d_θ per source<br>• `weights`: source weights (Default: None → equal; 2-D uses `TWO_DIMENSIONAL_SOURCE_WEIGHTS`) | `d = random_incidence_diffusion(d_thetas, weights=TWO_DIMENSIONAL_SOURCE_WEIGHTS)` |
| `TWO_DIMENSIONAL_SOURCE_WEIGHTS` | `tuple` | **ISO 17497-2 single-plane source weights.**<br>(1, 3, 3, 3, 3) for 0°, ±30°, ±60° | `TWO_DIMENSIONAL_SOURCE_WEIGHTS` |
| `ScatteringDiffusionWarning` | `warning class` | **ISO 17497 advisory.**<br>Emitted for out-of-range scattering/diffusion measurement conditions (e.g. a base plate over the Table 1 limits) | `warnings.simplefilter('error', ScatteringDiffusionWarning)` |
| `adrienne_window` | `function` | **Adrienne temporal window (ISO 13472-1 Clause 6.4).**<br>• `fs` [Hz]<br>• `flat_duration` [s] (Default: 0.005)<br>• `leading_duration` [s] (Default: 0.0005), `trailing_duration` [s] (Default: 0.005)<br>• `leading_edge`/`trailing_edge`: 'blackman-harris' or 'cosine-squared' | `w = adrienne_window(48000)`<br><br>• Rising edge + flat top + falling edge, peak 1.0 |
| `geometric_spreading_factor` | `function` | **Geometrical-spreading factor Kr (Clause 4.1).**<br>• `source_height` ds [m] (Default: 1.25)<br>• `mic_height` dm [m] (Default: 0.25) | `geometric_spreading_factor()  # 0.6667`<br><br>• Kr = (ds − dm)/(ds + dm) |
| `geometric_spreading_factor_angle` | `function` | **Oblique factor Kr,θ (Annex F).**<br>• `incidence_angle` θ [rad]<br>• `source_height`, `mic_height` | `geometric_spreading_factor_angle(np.pi/6)  # 0.764` |
| `reflected_path_delay` | `function` | **Reflected-path delay Δτ = 2dm/c (Annex C).**<br>• `mic_height` dm [m] (Default: 0.25)<br>• `speed_of_sound` c [m/s] (Default: 340.0) | `reflected_path_delay()  # 0.001471`<br><br>• [s] |
| `insitu_reflection_factor` | `function` | **Complex reflection factor r(f) (ISO 13472-1 Clause 4.1).**<br>• `incident_ir` / `reflected_ir`: windowed impulse responses<br>• `source_height`, `mic_height` [m]<br>• `incidence_angle` [rad] (Default: 0)<br>• `fs` + `delay`: undo the reflected-path offset (Default: None)<br>• `n`: FFT length | `r = insitu_reflection_factor(hi, hr, fs=48000, delay=dtau)`<br><br>• (1/Kr)·Hr(f)/Hi(f) at the rfft bins |
| `insitu_absorption_from_reflection` | `function` | **α from the reflection factor (Clause 4.1).**<br>• `reflection`: complex r | `alpha = insitu_absorption_from_reflection(r)`<br><br>• α = 1 − \|r\|² |
| `power_reflection_coefficient` | `function` | **Power reflection factor QW(f), direct energy route.**<br>• `incident_ir`, `reflected_ir`<br>• `source_height`, `mic_height`, `incidence_angle`, `n` | `qw = power_reflection_coefficient(hi, hr)`<br><br>• (1/Kr²)\|Hr/Hi\|², offset-independent |
| `insitu_absorption_coefficient` | `function` | **Narrow-band absorption α(f) (Clause 4.1).**<br>• Same parameters as `power_reflection_coefficient` | `alpha = insitu_absorption_coefficient(hi, hr)`<br><br>• α = 1 − QW(f) |
| `one_third_octave_absorption` | `function` | **Aggregate narrow-band α into one-third octaves.**<br>• `frequency` [Hz], `absorption`<br>• `f_min` (Default: 250), `f_max` (Default: 4000; 1600 for Part 2) [Hz]<br>• `clip_negative` (Default: True) | `fc, ab = one_third_octave_absorption(f, alpha)`<br><br>• Band centres + linear-averaged α (nan if empty) |
| `insitu_absorption_spectrum` | `function` | **End-to-end in-situ spectrum (ISO 13472-1).**<br>• `incident_ir`, `reflected_ir`, `fs` [Hz]<br>• geometry + `incidence_angle`<br>• `f_min`/`f_max` [Hz], `clip_negative` | `res = insitu_absorption_spectrum(hi, hr, 48000)`<br><br>• `InsituAbsorptionResult` |
| `InsituAbsorptionResult` | `dataclass` | **In-situ absorption spectrum.**<br>• `frequencies`: one-third-octave centres [Hz]<br>• `absorption`: α per band (nan when empty)<br>• `.plot()` | `res.absorption` |
| `absorption_reference_corrected` | `function` | **Reference-corrected road absorption (Annex B).**<br>• `road_reflection` / `reference_reflection`: measured Qp (complex, same geometry) | `alpha = absorption_reference_corrected(q_road, q_ref)`<br><br>• 1 − \|Qp,road/Qp,ref\|²; removes chain error and Kr |
| `max_sampled_area_radius` | `function` | **Maximum sampled-area radius (Annex A).**<br>• `window_width` Tw [s]<br>• `source_height`, `mic_height`, `speed_of_sound` | `max_sampled_area_radius(0.005)  # 1.34`<br><br>• [m], the Annex A worked example |
| `msa_major_axis` | `function` | **Major axis of the oblique sampled ellipsoid (Annex F).**<br>• `window_width` Tw [s]<br>• `projected_distance` dp [m]<br>• `source_height`, `mic_height`, `speed_of_sound` | `msa_major_axis(0.005, 0.0)  # 3.2`<br><br>• a = cTw + √((ds + dm)² + dp²) [m] |
| `spot_tube_upper_frequency` | `function` | **Spot-tube upper frequency (ISO 13472-2 §5.4.1).**<br>• `diameter` d [m]<br>• `speed_of_sound` (Default: 340.0) | `spot_tube_upper_frequency(0.1)  # 1972`<br><br>• f_u = 0.58c0/d [Hz] |
| `spot_microphone_spacing_bounds` | `function` | **Spacing bounds (s_min, s_max) (§5.4.2).**<br>• `speed_of_sound` (Default: 340.0)<br>• `f_min` (Default: 220), `f_max` (Default: 1800) [Hz] | `spot_microphone_spacing_bounds()  # (0.0773, 0.085)`<br><br>• [m], brackets the nominal 81 mm |
| `check_spot_frequency_range` | `function` | **Advise outside 250–1600 Hz (ISO 13472-2 Scope).**<br>• `frequency` [Hz] | `check_spot_frequency_range(f)`<br><br>• `RoadAbsorptionWarning` out of range |
| `spot_internal_loss_correction` | `function` | **Internal-loss (system) correction (Annex A).**<br>• `measured_absorption`, `system_absorption`: same bands<br>• `clip_negative` (Default: True) | `spot_internal_loss_correction([0.12, 0.10], [0.02, 0.03])  # [0.1, 0.07]`<br><br>• Subtractive Part-2 correction |
| `DEFAULT_SOURCE_HEIGHT` | `float` | **ISO 13472-1 mandatory source height ds [m].**<br>1.25 | `DEFAULT_SOURCE_HEIGHT  # 1.25` |
| `DEFAULT_MIC_HEIGHT` | `float` | **ISO 13472-1 mandatory microphone height dm [m].**<br>0.25 | `DEFAULT_MIC_HEIGHT  # 0.25` |
| `DEFAULT_SPEED_OF_SOUND` | `float` | **Default speed of sound for the road methods [m/s].**<br>340.0 | `DEFAULT_SPEED_OF_SOUND  # 340.0` |
| `PART1_FREQUENCY_RANGE` | `tuple` | **ISO 13472-1 valid band range [Hz].**<br>(250.0, 4000.0) | `PART1_FREQUENCY_RANGE` |
| `SPOT_FREQUENCY_RANGE` | `tuple` | **ISO 13472-2 valid band range [Hz].**<br>(250.0, 1600.0) | `SPOT_FREQUENCY_RANGE` |
| `SPOT_NARROW_BAND_RANGE` | `tuple` | **ISO 13472-2 narrow-band range [Hz].**<br>(220.0, 1800.0) | `SPOT_NARROW_BAND_RANGE` |
| `RoadAbsorptionWarning` | `warning class` | **ISO 13472 advisory.**<br>Emitted for frequencies outside the valid in-situ road-absorption ranges; results there are advisory | `warnings.simplefilter('error', RoadAbsorptionWarning)` |
| `frequency_weighting` | `function` | **Vibration frequency weighting H(f) (ISO 8041-1:2017 Formula 5).**<br>• `name`: one of `WEIGHTING_NAMES`<br>• `frequencies` [Hz] (> 0) | `wr = frequency_weighting('Wk', [1.0, 8.0, 63.0])`<br><br>• `WeightingResponse`; \|H\| = [0.482, 1.036, 0.186] |
| `weighting_factors` | `function` | **Weighting factors \|H(f)\| (the Wi of ISO 2631-1 Eq. 9).**<br>• `name`, `frequencies` [Hz] | `weighting_factors('Wh', [16.0])`<br><br>• Magnitude per frequency |
| `apply_weighting` | `function` | **Apply a weighting to a time signal (frequency domain, exact response).**<br>• `signal`: acceleration (1D) [m/s²]<br>• `fs` [Hz]<br>• `name`: one of `WEIGHTING_NAMES` | `aw_t = apply_weighting(a, fs, 'Wk')`<br><br>• Weighted signal, same length (circular FFT filtering) |
| `WeightingResponse` | `dataclass` | **Weighting response.**<br>• `name`<br>• `frequencies` [Hz]<br>• `response`: complex H<br>• `magnitude`, `magnitude_db` [dB]<br>• `.plot()` | `wr.magnitude, wr.magnitude_db` |
| `WEIGHTING_NAMES` | `tuple` | **ISO 8041-1 weighting names.**<br>('Wb', 'Wc', 'Wd', 'We', 'Wf', 'Wh', 'Wj', 'Wk', 'Wm') | `'Wk' in WEIGHTING_NAMES  # True` |
| `weighted_acceleration` | `function` | **Weighted r.m.s. from a band spectrum (ISO 2631-1 Eq. 9 / ISO 5349-1 Eq. A.1).**<br>• `band_accelerations`: ai per band [m/s²]<br>• `frequencies`: band centres [Hz]<br>• `weighting`: name | `ws = weighted_acceleration([0.1, 0.3, 0.2], [4.0, 8.0, 16.0], 'Wk')`<br><br>• `WeightedSpectrum`; aw = 0.36 m/s² |
| `WeightedSpectrum` | `dataclass` | **Weighted band spectrum.**<br>• `frequencies` [Hz], `band_accelerations` [m/s²]<br>• `weighting_name`, `weighting_factors`<br>• `weighted`: Wi·ai [m/s²]<br>• `overall`: aw [m/s²]<br>• `.plot()` | `ws.overall` |
| `running_rms` | `function` | **Running r.m.s. of a weighted signal (ISO 2631-1 Eqs. 2/3).**<br>• `signal` [m/s²], `fs` [Hz]<br>• `integration_time` τ [s] (Default: 1.0)<br>• `method`: 'linear' (Eq. 2) or 'exponential' (Eq. 3) (Default: 'linear') | `env = running_rms(aw_t, fs)`<br><br>• aw(t0) per sample [m/s²] |
| `mtvv` | `function` | **Maximum transient vibration value (Eq. 4).**<br>• `signal` [m/s²], `fs` [Hz]<br>• `integration_time` [s] (Default: 1.0) | `mtvv(aw_t, fs)`<br><br>• max aw(t0) [m/s²] |
| `vibration_dose_value` | `function` | **Vibration dose value VDV (Eq. 5).**<br>• `signal`: weighted acceleration [m/s²]<br>• `fs` [Hz] | `vdv = vibration_dose_value(aw_t, fs)`<br><br>• (∫aw⁴dt)^(1/4) [m/s^1.75] |
| `motion_sickness_dose_value` | `function` | **Motion sickness dose value MSDV (ISO 2631-1 clause 9).**<br>• `signal`: Wf-weighted acceleration [m/s²]<br>• `fs` [Hz] | `msdv = motion_sickness_dose_value(aw_t, fs)`<br><br>• (∫aw²dt)^(1/2) [m/s^1.5] |
| `crest_factor` | `function` | **Crest factor of a weighted signal (clause 6.2.1).**<br>• `signal` [m/s²] | `crest_factor(aw_t)`<br><br>• peak/r.m.s.; `HumanVibrationWarning` above 9 |
| `vibration_total_value` | `function` | **Vibration total value av/ahv (ISO 2631-1 Eq. 10).**<br>• `components`: axis-weighted r.m.s. [m/s²]<br>• `k`: per-axis factors (Default: None → 1, the ISO 5349-1 vector sum) | `vibration_total_value([0.3, 0.4, 0.5], k=[1.4, 1.4, 1.0])  # 0.86`<br><br>• √(Σ kj²awj²) [m/s²] |
| `daily_exposure` | `function` | **Daily exposure A(8) for one operation (ISO 5349-1 Eq. 2).**<br>• `total_value`: ahv or av [m/s²]<br>• `duration_s`: T [s] | `daily_exposure(3.0, 4*3600)  # 2.12`<br><br>• ahv √(T/8h) [m/s²] |
| `partial_exposure` | `function` | **Partial exposure Ai(8) of one operation (Eq. 2).**<br>• `total_value` [m/s²], `duration_s` [s] | `partial_exposure(3.0, 2*3600)  # 1.5` |
| `combine_partial_exposures` | `function` | **Combine partial exposures (Eq. 3).**<br>• `partials`: Ai(8) [m/s²] | `combine_partial_exposures([1.5, 2.1])  # 2.58`<br><br>• √(Σ Ai(8)²) [m/s²] |
| `hav_daily_exposure` | `function` | **A(8) for several operations (ISO 5349-1 Eq. 3).**<br>• `total_values`: ahvi [m/s²]<br>• `durations_s`: Ti [s] | `hav_daily_exposure([3.0, 5.0], [2*3600, 3600])  # 2.32` |
| `energy_equivalent_acceleration` | `function` | **Energy-equivalent magnitude aw,e (ISO 2631-1 Eq. B.3).**<br>• `magnitudes` [m/s²], `durations_s` [s] | `energy_equivalent_acceleration([0.5, 1.0], [3600, 1800])  # 0.707` |
| `hav_vwf_lifetime_years` | `function` | **Years to 10 % vibration-white-finger prevalence (ISO 5349-1 Eq. C.1).**<br>• `a8`: A(8) [m/s²] (> 0) | `hav_vwf_lifetime_years(2.5)  # 12.0`<br><br>• Dy = 31.8 A(8)^−1.06 [years] |
| `exposure_assessment` | `function` | **Assess a daily exposure (Directive 2002/44/EC Article 3).**<br>• `value`: A(8) [m/s²] or VDV [m/s^1.75]<br>• `kind`: 'hav'/'wbv'<br>• `metric`: 'a8' (Default) or 'vdv' (whole-body only) | `ea = exposure_assessment(3.0, kind='hav')`<br><br>• `ExposureAssessment` (zone 'action') |
| `ExposureAssessment` | `dataclass` | **Directive assessment.**<br>• `value`, `kind`, `metric`<br>• `action_value` (EAV), `limit_value` (ELV)<br>• `exceeds_action`, `exceeds_limit`<br>• `zone`: 'below action'/'action'/'limit' | `ea.zone, ea.exceeds_limit` |
| `daily_vibration_exposure` | `function` | **A(8) from several operations, assessed (ISO 5349 + Directive).**<br>• `total_values` [m/s²], `durations_s` [s]<br>• `kind`: 'hav'/'wbv'<br>• `labels` (Default: None → 'op 1', …) | `res = daily_vibration_exposure([3.0, 5.0], [2*3600, 3600], kind='hav')`<br><br>• `DailyVibrationExposure` (A(8) = 2.32) |
| `DailyVibrationExposure` | `dataclass` | **Assessed daily exposure.**<br>• `a8` [m/s²]<br>• `labels`, `total_values`, `durations_s`, `partials`<br>• `assessment`: `ExposureAssessment`<br>• `.plot()` | `res.a8, res.assessment.zone` |
| `HumanVibrationWarning` | `warning class` | **Human-vibration advisory.**<br>Emitted for a crest factor above 9 (ISO 2631-1 6.2.2) or other out-of-range measurement conditions | `warnings.simplefilter('error', HumanVibrationWarning)` |
| `REFERENCE_ACCELERATION` | `float` | **Vibration reference acceleration [m/s²].**<br>1e-6 (ISO 1683 acceleration level reference) | `REFERENCE_ACCELERATION  # 1e-06` |
| `REFERENCE_DURATION_S` | `float` | **Daily-exposure reference duration T0 [s].**<br>28800 (8 h) | `REFERENCE_DURATION_S  # 28800.0` |
| `HAV_EAV_A8` | `float` | **Hand-arm exposure action value [m/s²].**<br>2.5 (Directive 2002/44/EC) | `HAV_EAV_A8  # 2.5` |
| `HAV_ELV_A8` | `float` | **Hand-arm exposure limit value [m/s²].**<br>5.0 | `HAV_ELV_A8  # 5.0` |
| `WBV_EAV_A8` | `float` | **Whole-body A(8) action value [m/s²].**<br>0.5 | `WBV_EAV_A8  # 0.5` |
| `WBV_ELV_A8` | `float` | **Whole-body A(8) limit value [m/s²].**<br>1.15 | `WBV_ELV_A8  # 1.15` |
| `WBV_EAV_VDV` | `float` | **Whole-body VDV action value [m/s^1.75].**<br>9.1 | `WBV_EAV_VDV  # 9.1` |
| `WBV_ELV_VDV` | `float` | **Whole-body VDV limit value [m/s^1.75].**<br>21.0 | `WBV_ELV_VDV  # 21.0` |
| `PhonometryWarning` | `warning class` | **Base class for all phonometry warnings.**<br>Catch or silence every library advisory at once | `warnings.simplefilter('error', PhonometryWarning)` |
| `FilterBankWarning` | `warning class` | **Fractional-octave filter-bank advisory.**<br>Emitted for filter-bank processing pitfalls | `warnings.simplefilter('error', FilterBankWarning)` |
| `TonalityWarning` | `warning class` | **Tonality advisory.**<br>Emitted for biased tonality estimates (e.g. coarse FFT resolution) | `warnings.simplefilter('error', TonalityWarning)` |
| `STIWarning` | `warning class` | **STI/STIPA advisory.**<br>Emitted for suspect speech-intelligibility measurements or inputs | `warnings.simplefilter('error', STIWarning)` |
| `__version__` | `str` | **Package version string.**<br>(no parameters) | `phonometry.__version__  # '3.0.0'` |
| `.plot()` | `method` | **One-line canonical figure on every result object (soft matplotlib dependency).**<br>Available on `ZwickerLoudness`, `MooreGlasbergLoudness`, `MooreGlasbergTimeVaryingLoudness`, `EcmaLoudness`, `EcmaTonality`, `EcmaRoughness`, `STIResult`, `SIIResult`, `NCResult`, `RCResult`, `AgeThresholdResult`, `NiptsResult`, `HtlanResult`, `ImpulseProminenceResult`, `MultipleShockResult`, `ImpulseResponseResult`, `DecayCurve`, `RoomAcousticsResult`, `ReverberationResult`, `WeightedRatingResult`, `ImpactRatingResult`, `FacadeInsulationResult`, `LabAirborneInsulationResult`, `LabImpactInsulationResult`, `SoundPowerResult`, `ReverberationSoundPowerResult`, `SoundPowerIntensityResult`, `PrecisionSoundPowerResult`, `PrecisionIntensityResult`, `IntensityResult`, `UncertaintyResult`, `AbsorptionRatingResult`, `ScatteringResult`, `DiffusionResult`, `InsituAbsorptionResult`, `WeightingResponse`, `WeightedSpectrum` and `DailyVibrationExposure`.<br>• `ax`: existing Axes, or None to build a fresh figure (Default: None)<br>• returns the Matplotlib `Axes` (an array of Axes for multi-panel figures); never calls `plt.show()`<br>• needs matplotlib (`pip install phonometry[plot]`) | `res.plot()`<br>`decay_curve(ir, fs).plot()` |

## Notes

- `zero_phase=True` (in `OctaveFilterBank.filter` and `spectrogram`) filters
  forward-backward (`sosfiltfilt`): no group delay, doubled effective
  attenuation, offline analysis only. Incompatible with `stateful=True`. The
  passband also narrows, lowering the measured broadband band level by ~0.2 to
  0.3 dB per band (a pure in-band tone is unaffected); prefer forward filtering
  when the absolute band SPL must match single-pass conventions, and reserve
  zero-phase for when the temporal envelope matters (e.g. reverberation decay).
- `mode='peak'` includes the filter's onset transient; a tone that starts
  abruptly can overshoot by ~1 dB. See [Calibration and dBFS](/phonometry/guides/calibration/).
- `octave_filter()` caches filter bank designs internally (32 entries), so
  repeated calls with the same parameters skip the design phase. For explicit
  control use `OctaveFilterBank`.
- Deprecated aliases (kept for one cycle, warn on use, removal in 4.0):
  `octavefilter` → `octave_filter`, `getansifrequencies` →
  `nominal_frequencies`, `normalizedfreq` → `normalized_frequencies`,
  `calculate_sensitivity` → `sensitivity`, `coverage_factor` →
  `insulation_coverage_factor`, `expanded_uncertainty` →
  `insulation_expanded_uncertainty`, plus the renamed names
  `OCTAVE_BANDS_HZ` → `OCTAVE_BANDS`, `THIRD_OCTAVE_BANDS_HZ` →
  `THIRD_OCTAVE_BANDS`, `BASE_PLATE_BANDS_HZ` → `BASE_PLATE_BANDS` and
  `ExposureWarning` → `OccupationalExposureWarning`.
