Source: https://jmrplens.github.io/phonometry/signals/levels/special-weightings/ # Special Weightings (G, B, D, AU) Beyond A, C and Z, the weighting family keeps four special-purpose curves, each the right tool for a narrower job: the **G** curve of **ISO 7196:1995** rates infrasound below 20 Hz the way A-weighting rates audible noise, the historical **B** (ANSI S1.4-1983) reproduces measurements taken under older national codes, the withdrawn aircraft-noise **D** (IEC 537) serves comparisons with legacy data, and **AU** (IEC 61012), still in force like the G curve, keeps ultrasonic components out of an audible-exposure reading. All four share the machinery of the IEC 61672-1 curves (0 dB at 1 kHz where applicable, multichannel and stateful block processing), and B, D and AU also take the `high_accuracy` oversampling, and G takes it too: **the default G design oversamples toward 48 kHz**, so its 0.25 Hz to 315 Hz range stays within about 0.05 dB whatever the input rate, while stateful block processing runs the plain design at the input rate, about a decibel low at 315 Hz at fs = 2000 and exactly on the 0 dB reference at 10 Hz. That matters exactly where G is used — infrasound is often recorded at 1 kHz or 2 kHz, where 315 Hz sits close to Nyquist and the bilinear warping grows quadratically; at audio rates the correction is negligible. As with A/C/Z, `high_accuracy` cannot be combined with stateful processing. The A, C and Z curves themselves, where they come from, the `high_accuracy` design and the class verification against IEC 61672-1 Table 3 are the subject of [Frequency Weighting](https://jmrplens.github.io/phonometry/signals/levels/weighting/). ## 1. Infrasound: G-weighting (ISO 7196) The **G frequency weighting** (ISO 7196:1995) rates infrasound the way A-weighting rates audible noise. It is defined by a pole-zero configuration with 0 dB gain at 10 Hz, rises at 12 dB/octave from 1 Hz to 20 Hz (matching the steep growth of perception in that band) and falls off at 24 dB/octave outside it. Use it for sources with significant energy below 20 Hz (wind turbines, HVAC, blasting): ```python import numpy as np from phonometry import filters # recording: a calibrated microphone capture (Pa) — recorded through your measurement chain. Synthesized here so the guide runs standalone. fs = 48000 recording = 0.2 * np.sin(2 * np.pi * 1000 * np.arange(fs) / fs) g_weighted = filters.weighting_filter(recording, fs, curve='G') ```

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```python import matplotlib.pyplot as plt import numpy as np from phonometry import filters # Measure the G response: weight a centered unit impulse and take its # spectrum. A long buffer gives the resolution the infrasound range # needs (20 s -> 0.05 Hz). fs = 4000 impulse = np.zeros(20 * fs) impulse[impulse.size // 2] = 1.0 freqs = np.fft.rfftfreq(impulse.size, 1 / fs) spectrum = np.fft.rfft(filters.weighting_filter(impulse, fs, curve="G")) fig, ax = plt.subplots(figsize=(9, 5)) ax.semilogx(freqs[1:], 20 * np.log10(np.abs(spectrum[1:]) + np.finfo(float).eps)) ax.plot(10, 0, "o", color="tab:red", label="0 dB at 10 Hz") ax.set(xlim=(0.1, 1000), ylim=(-90, 15), xlabel="Frequency [Hz]", ylabel="G-weighting response [dB]") ax.grid(True, which="both", alpha=0.3) ax.legend() plt.show() ```

The implementation follows the ISO 7196 Table 1 pole/zero values exactly and is verified in CI against every Table 2 nominal response value (0.25 Hz to 315 Hz). `WeightingFilter(fs, "G")` supports the same multichannel and stateful block processing as A/C — but stateful mode cannot carry the internal oversampling across blocks, so if you stream G-weighting at a sample rate below 48 kHz, verify the response before trusting the level. Levels measured with the G curve are reported as $L_{p\mathrm{G}}$ (or $L_\mathrm{Geq}$ for the equivalent level over time). ## 2. Historical and special-purpose curves: B, D and AU Three more curves complete the family. All three work in the audible range, so they share one chart, drawn against the A curve because that is what each of them is defined or described against: B as the curve between A and C, D as the one with a hump A does not have, AU as A itself with a low-pass added. *The three curves against the A reference (wide grey), measured at 96 kHz so the axis reaches the 40 kHz where IEC 61012 still specifies the U low-pass. B (green, dashed) discards less bass than A; D (purple) carries the +11.5 dB hump at 3.15 kHz where jet turbomachinery whine annoys most; AU (orange) runs inside the A reference up to 10 kHz and then falls away with U, reaching 13 dB below A at 16 kHz. The infrasound G curve keeps its own chart in section 1, and A, C and Z are in [Frequency Weighting](https://jmrplens.github.io/phonometry/signals/levels/weighting/).*

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```python import matplotlib.pyplot as plt import numpy as np from phonometry import filters # Measure each curve's response: weight a centered unit impulse and take its # spectrum. 96 kHz, not 48 kHz: it reaches the 40 kHz top row of the # IEC 61012 U-weighting table, which is the whole point of AU. fs = 96000 impulse = np.zeros(fs) impulse[fs // 2] = 1.0 freqs = np.fft.rfftfreq(fs, 1 / fs) fig, ax = plt.subplots(figsize=(9, 5)) # A goes first and wide, as the reference the other three are read against. for curve, width in (("A", 4.0), ("B", 1.8), ("D", 1.8), ("AU", 1.8)): spectrum = np.fft.rfft(filters.weighting_filter(impulse, fs, curve=curve)) ax.semilogx(freqs[1:], 20 * np.log10(np.abs(spectrum[1:]) + np.finfo(float).eps), label=curve, linewidth=width) ax.set(xlim=(10, 40000), ylim=(-90, 18), xlabel="Frequency [Hz]", ylabel="Response [dB]") ax.grid(True, which="both", alpha=0.3) ax.legend() plt.show() ```

### B (ANSI S1.4-1983, historical) The middle curve of the original A/B/C level-switching scheme, drawn from the ~70-phon equal-loudness contour. Analytically it is the C weighting with one more zero at the origin and one extra real pole at $f_5 = 158.49\ \text{Hz}$ (Appendix C of ANSI S1.4-1983), so it discards less bass than A and more than C. It was dropped when IEC 61672-1 replaced the older sound-level-meter standards; use it only to reproduce historical data and measurements taken under older national codes (some legacy automotive test procedures reported dB(B)). The implementation follows the ANSI S1.4-1983 Appendix C constants and is pinned in CI against the Table IV response values, within the strictest Table V mask (Type 0). ### D (IEC 537, withdrawn: aircraft noise) The D weighting approximated the *perceived noisiness* contours used by the perceived-noise-level (PNL) rating, so a plain sound level meter could estimate aircraft noise: the +11.5 dB hump around 3.15 kHz is where jet turbomachinery whine annoys most (it is deliberately *not* an equal-loudness feature). NASA's aircraft-noise handbook gives the classic rule of thumb $L_\mathrm{PN} \approx L_\mathrm{D} + 7\ \text{dB}$. IEC 537 was withdrawn and current certification practice reports EPNL from one-third-octave analysis or plain A-weighted levels, so `D` is provided for historical data and comparisons. With the standard unavailable, the implementation uses the widely published IEC 537 rational transfer function and is cross-checked against two independent implementations (SQAT's zeros/poles and librosa's closed form, which agree within 0.002 dB) and pinned in CI against the IEC 537 table republished in NASA CR-3406. ```python import numpy as np from phonometry import filters, signals # A 3.15 kHz whine sits right on the D-weighting hump: D rates it # 10 dB *louder* than A does. fs = 96000 t = np.arange(fs) / fs whine = 0.1 * np.sin(2 * np.pi * 3150 * t) ld = signals.leq(filters.weighting_filter(whine, fs, curve="D")) la = signals.leq(filters.weighting_filter(whine, fs, curve="A")) print(f"LD = {ld:.1f} dB LA = {la:.1f} dB") # LD = 82.5 dB LA = 72.2 dB ``` ### AU (IEC 61012, current: audible sound in the presence of ultrasound) The only one of the three still in force. `AU` is the A weighting cascaded with the **U** low-pass filter of IEC 61012:1990 (six poles, Table 2): flat relative to A up to 10 kHz, then a steep cutoff (-13 dB at 16 kHz, -61.8 dB at 40 kHz for U alone). Use it when strong ultrasonic components (ultrasonic cleaners and welders, rodent repellers, some public-space deterrents) would otherwise leak into an A-weighted reading through the meter's imperfect high-frequency roll-off and overstate the *audible* exposure: ```python import numpy as np from phonometry import filters, signals # 1 kHz tone (audible) buried under a strong 25 kHz ultrasonic component. fs = 96000 t = np.arange(fs) / fs audible = 0.1 * np.sin(2 * np.pi * 1000 * t) x = audible + 1.0 * np.sin(2 * np.pi * 25000 * t) la = signals.leq(filters.weighting_filter(x, fs, curve="A")) lau = signals.leq(filters.weighting_filter(x, fs, curve="AU")) la_ref = signals.leq(filters.weighting_filter(audible, fs, curve="A")) print(f"LA = {la:.1f} dB LAU = {lau:.1f} dB audible alone = {la_ref:.1f} dB") # LA = 78.6 dB LAU = 71.0 dB audible alone = 71.0 dB # The ultrasound inflates LA by 7.6 dB; AU recovers the audible level. ``` Ultrasound only reaches a digital filter when the sample rate captures it, so measure at 96 kHz or more (at 48 kHz there is nothing above 24 kHz to reject); the AU design internally oversamples toward 288 kHz to keep the steep U roll-off accurate. Levels are reported as $L_\mathrm{AU}$. The implementation follows the Table 2 pole locations exactly (they reproduce every Table 1 nominal value within 0.05 dB) and is verified in CI against the Table 1 tolerances up to 40 kHz. ## 3. Verifying B and AU against their tolerance tables The `verify_weighting_class` verifier, described in section 6 of [Frequency Weighting](https://jmrplens.github.io/phonometry/signals/levels/weighting/), also covers the curves of this guide that have published tolerance tables. For `B` it uses ANSI S1.4-1983 (Table IV design goals, Table V limits) and the "class" verdicts read as the standard's instrument **Types** 1 and 2. For `AU` it uses IEC 61012:1990 Table 1 (nominal A + nominal U with the separate-unit tolerances, zero at the 1 kHz reference); IEC 61012 publishes a single tolerance set, so both margin slots agree and the verdict is simply complies (1) or not (`None`) — note that checking the rows above 20 kHz needs `fs` ≥ 96 kHz (below that they are dropped and the verdict is `range_limited`). `G` and `D` are rejected: ISO 7196 defines one ±1 dB tolerance with no class structure, and the withdrawn IEC 537 left no tolerance table behind (both curves are pinned numerically in the CI conformance report instead). ## Quick answers ### Which weighting should I use for infrasound below 20 Hz? Use the G frequency weighting of ISO 7196:1995, which rates infrasound the way A-weighting rates audible noise. It has 0 dB gain at 10 Hz, rises at 12 dB/octave from 1 Hz to 20 Hz and falls off at 24 dB/octave outside that band. Apply it to sources such as wind turbines, HVAC and blasting, and report levels as $L_{p\mathrm{G}}$ (or $L_\mathrm{Geq}$ for the equivalent level over time). ## See also - [Frequency Weighting](https://jmrplens.github.io/phonometry/signals/levels/weighting/): the A, C and Z curves, the `high_accuracy` design and the IEC 61672-1 Table 3 class verification these curves build on. - API reference: [`filters.weighting`](https://jmrplens.github.io/phonometry/reference/api/filters/weighting/) and [`filters.compliance`](https://jmrplens.github.io/phonometry/reference/api/filters/compliance/). ## References - International Organization for Standardization. (1995). *Acoustics — Frequency-weighting characteristic for infrasound measurements* (ISO 7196:1995). [iso.org catalogue](https://www.iso.org/standard/13813.html). The G-weighting pole/zero definition (Table 1), verified against every Table 2 nominal response value (0.25 Hz to 315 Hz). - American National Standards Institute. (1983). *Specification for Sound Level Meters* (ANSI S1.4-1983). The historical B weighting: Appendix C analytic definition (Formula C2), Table IV design goals and Table V tolerance limits checked by `verify_weighting_class` in section 3. - International Electrotechnical Commission. (1990). *Filters for the measurement of audible sound in the presence of ultrasound* (IEC 61012:1990). [IEC webstore](https://webstore.iec.ch/en/publication/4296). The AU weighting: U-weighting pole locations (Table 2), nominal responses and tolerances (Table 1) and the combined AU definition of subclause 2.2. - International Electrotechnical Commission. (1976). *Frequency weighting for the measurement of aircraft noise (D-weighting)* (IEC 537:1976, withdrawn). Implemented from its published rational transfer function and cross-checked against independent implementations (section 2). - Bennett, R. L., & Pearsons, K. S. (1981). *Handbook of Aircraft Noise Metrics* (NASA CR-3406). NASA. [ntrs.nasa.gov](https://ntrs.nasa.gov/citations/19810013341). Republishes the IEC 537 D-weighting table (Table SLD-I) used to pin the D response in CI. ## Standards ISO 7196:1995, *Acoustics — Frequency-weighting characteristic for infrasound measurements*: the G-weighting pole/zero definition (Table 1), verified against every Table 2 nominal response value (0.25 Hz to 315 Hz). ANSI S1.4-1983, *Specification for Sound Level Meters*: the historical B weighting (Appendix C, Tables IV and V). IEC 61012:1990, *Filters for the measurement of audible sound in the presence of ultrasound*: the AU weighting (Tables 1 and 2, subclause 2.2). IEC 537:1976 (withdrawn), *Frequency weighting for the measurement of aircraft noise*: the D weighting, from its published rational transfer function.