metrology.parametric_filters

Weighting filters (A, B, C, D, G, AU, Z) and time weighting utilities.

A/C/Z per IEC 61672-1:2013; G (infrasound) per ISO 7196:1995.

B is the historical weighting of ANSI S1.4-1983 (Appendix C): the C curve with one extra zero at the origin and one extra real pole at f5 = 158.48932 Hz. It was dropped from the sound-level-meter standards when IEC 61672-1 replaced IEC 60651 (first edition 2002) and is provided for historical data and older national codes only.

AU per IEC 61012:1990: the A weighting cascaded with the U low-pass (six poles, Table 2: a double real pole at -12 200 Hz and complex pairs at -7 850 +/- j8 800 Hz and -2 900 +/- j12 150 Hz) for measuring audible sound in the presence of ultrasound. It is flat relative to A up to 10 kHz and cuts steeply above (U alone, Table 1: -2.8 dB at 12.5 kHz; -61.8 dB at 40 kHz). The Table 2 poles reproduce every Table 1 nominal value within 0.05 dB.

D per the withdrawn IEC 537:1976 (aircraft-noise weighting): implemented from the widely published rational transfer function k s (s^2 + 6532 s + 4.0975e7) / ((s + 1776.3)(s + 7288.5) (s^2 + 21514 s + 3.8836e8)), with k renormalized to exactly 0 dB at 1 kHz. The standard itself is withdrawn and unavailable, so the constants are corroborated against two independent implementations: SQAT (sound_level_meter/Gen_weighting_filters.m: identical zeros and poles; note its display-only freqResp line prints 1773.6 where its pole list, and every other source, has 1776.3) and librosa (librosa.D_weighting, an independent frequency-domain closed form; agreement within 0.002 dB from 10 Hz to 20 kHz). The response also reproduces the tabulated IEC 537 curve republished in the NASA Handbook of Aircraft Noise Metrics (NASA CR-3406, 1981, Table SLD-I) within 0.1 dB at every one-third-octave frequency from 50 Hz to 10 kHz except 1600 Hz (0.15 dB) and 2500 Hz (0.28 dB), where that table appears to round a different source curve.

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linkwitz_riley

linkwitz_riley(
    x: list[float] | np.ndarray,
    fs: int,
    freq: float,
    order: int = 4,
) -> tuple[np.ndarray, np.ndarray]

Linkwitz-Riley crossover filter (Butterworth squared). Splits signal into low and high bands with flat sum response.

Parameters

Name	Description
x	Input signal.
fs	Sample rate.
freq	Crossover frequency.
order	Total order (must be even, typically 2 or 4).

Returns: (low_pass_signal, high_pass_signal)

time_weighting

time_weighting(
    x: list[float] | np.ndarray,
    fs: int,
    mode: str = 'fast',
    initial_state: str | float | np.ndarray | None = None,
) -> np.ndarray

Apply time weighting to a signal (Exponential averaging).

Parameters

Name	Description
x	Input signal (raw pressure/voltage). The function squares it internally.
fs	Sample rate.
mode	’fast’ (125ms), ‘slow’ (1000ms), ‘impulse’ (35ms rise, 1500ms fall).
initial_state	Previous mean-square output state y[-1]. Use None/‘zero’ for zero initialization (default), ‘first’ to initialize from the first input energy, or a scalar/array broadcastable to the input shape without the time axis.

Returns: Time-weighted squared signal (sound pressure level envelope).

TimeWeighting

TimeWeighting(fs: int, mode: str = 'fast')

Stateful time weighting for block processing.

Wraps time_weighting carrying the exponential integrator state across blocks, so concatenated block outputs equal a single continuous call.

Parameters

Name	Description
fs	Sample rate in Hz.
mode	’fast’ (125 ms), ‘slow’ (1000 ms) or ‘impulse’ (35 ms / 1.5 s).

TimeWeighting.process()

TimeWeighting.process(x: list[float] | np.ndarray) -> np.ndarray

Apply time weighting to a block, continuing from the previous block.

TimeWeighting.reset()

TimeWeighting.reset() -> None

Forget the carried state (the next block starts from rest).

weighting_filter

weighting_filter(
    x: list[float] | np.ndarray,
    fs: int,
    curve: str = 'A',
    high_accuracy: bool = True,
) -> np.ndarray

Apply a frequency weighting to a signal.

Parameters

Name	Description
x	Input signal.
fs	Sample rate.
curve	’A’, ‘C’ (IEC 61672-1), ‘B’ (ANSI S1.4-1983, historical), ‘D’ (withdrawn IEC 537 aircraft-noise weighting), ‘G’ (ISO 7196 infrasound), ‘AU’ (IEC 61012) or ‘Z’ (bypass).
high_accuracy	Use internal oversampling for IEC 61672-1 class 1 accuracy at high frequencies (default True).

Returns: Weighted signal.

WeightingFilter

WeightingFilter(
    fs: int,
    curve: str = 'A',
    stateful: bool = False,
    steady_ic: bool = False,
    high_accuracy: bool | None = None,
)

Class-based frequency weighting filter (A, B, C, D, G, AU, Z). Allows pre-calculating and reusing filter coefficients.

Initialize the weighting filter.

Parameters

Name	Description
fs	Sample rate in Hz.
curve	’A’, ‘C’ (IEC 61672-1), ‘B’ (ANSI S1.4-1983, historical: removed from the IEC sound-level-meter standards), ‘D’ (withdrawn IEC 537 aircraft-noise weighting), ‘G’ (ISO 7196 infrasound), ‘AU’ (IEC 61012, audible sound in the presence of ultrasound) or ‘Z’.
stateful	If True, the weighting filter is stateful. Useful for block processing.
steady_ic	If True, calculate steady state initial conditions for filter.
high_accuracy	If True, design and run the filter at an internal oversampled rate (target >= 144 kHz) so the response stays within IEC 61672-1 class 1 tolerances up to 16 kHz. At 48 kHz this oversamples x3, keeping the deviation from the analytic curve to about -0.44 dB @16k / -0.85 dB @20k. The plain bilinear design still holds class 1 at fs = 44.1/48 kHz (about -2.7 dB at 12.5 kHz, inside the +2.0/-5.0 class 1 limits) but degrades to class 2 for fs <= 32 kHz. Defaults to True except in stateful mode (the internal FIR resampling is incompatible with block processing).

WeightingFilter.filter()

WeightingFilter.filter(x: list[float] | np.ndarray) -> np.ndarray

Apply the weighting filter to a signal.

Parameters

Name	Description
x	Input signal (1D or 2D [channels, samples]).

Returns: Weighted signal.