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iec_61672_1_2013

IEC 61672-1:2013

This module implements IEC 61672-1:2013 which provides electroacoustical performance specifications for three kinds of sound measuring instruments:

  1. Time-weighting sound level meters that measure exponential-time-weighted, frequency-weighted sound levels
  2. Integrating-averaging sound level meters that measure time-averaged, frequency-weighted sound levels
  3. Integrating sound level meters that measure frequency-weighted sound exposure levels

The module provides functions for: - Frequency weighting (A, C, Z) - Time weighting (Fast, Slow) - Sound level calculations

Reference

IEC 61672-1:2013: http://webstore.iec.ch/webstore/webstore.nsf/artnum/048669

Attributes

WEIGHTING_DATA module-attribute 

WEIGHTING_DATA = read_csv(
    BytesIO(
        get_data(
            "acoustic_toolbox",
            join("data", "iec_61672_1_2013.csv"),
        )
    ),
    sep=",",
    index_col=0,
)

DataFrame with indices, nominal frequencies and weighting values.

NOMINAL_THIRD_OCTAVE_CENTER_FREQUENCIES module-attribute 

NOMINAL_THIRD_OCTAVE_CENTER_FREQUENCIES: NDArray[
    float64
] = array(nominal)

Nominal ⅓-octave frequencies. See table 3.

NOMINAL_OCTAVE_CENTER_FREQUENCIES module-attribute 

NOMINAL_OCTAVE_CENTER_FREQUENCIES: NDArray[float64] = array(
    nominal
)[2::3]

Nominal 1/1-octave frequencies. Based on table 3.

REFERENCE_FREQUENCY module-attribute 

REFERENCE_FREQUENCY: float = 1000.0

Reference frequency. See table 3.

EXACT_THIRD_OCTAVE_CENTER_FREQUENCIES module-attribute 

EXACT_THIRD_OCTAVE_CENTER_FREQUENCIES: NDArray[float64] = (
    REFERENCE_FREQUENCY * 10.0**0.01 * arange(10, 44) - 30
)

Exact third-octave center frequencies. See table 3.

WEIGHTING_A module-attribute 

WEIGHTING_A: NDArray[float64] = array(A)

Frequency weighting A. See table 3.

WEIGHTING_C module-attribute 

WEIGHTING_C: NDArray[float64] = array(C)

Frequency weighting C. See table 3.

WEIGHTING_Z module-attribute 

WEIGHTING_Z: NDArray[float64] = array(Z)

Frequency weighting Z. See table 3.

WEIGHTING_VALUES module-attribute 

WEIGHTING_VALUES: Dict[str, NDArray[float64]] = {
    "A": WEIGHTING_A,
    "C": WEIGHTING_C,
    "Z": WEIGHTING_Z,
}

Dictionary with weighting values 'A', 'C' and 'Z' weighting.

FAST module-attribute 

FAST: float = 0.125

FAST time-constant.

SLOW module-attribute 

SLOW: float = 1.0

SLOW time-constant.

_POLE_FREQUENCIES module-attribute 

_POLE_FREQUENCIES: Dict[int, float] = {
    1: 20.6,
    2: 107.7,
    3: 737.9,
    4: 12194.0,
}

Approximate values for pole frequencies f_1, f_2, f_3 and f_4.

See section E.4.1 of the standard.

_NORMALIZATION_CONSTANTS module-attribute 

_NORMALIZATION_CONSTANTS: Dict[str, float] = {
    "A": -2.0,
    "C": -0.062,
}

Normalization constants \(C_{1000}\) and \(A_{1000}\).

See section E.4.2 of the standard.

WEIGHTING_FUNCTIONS module-attribute 

WEIGHTING_FUNCTIONS: Dict[str, callable] = {
    "A": weighting_function_a,
    "C": weighting_function_c,
    "Z": weighting_function_z,
}

Dictionary with available weighting functions 'A', 'C' and 'Z'.

WEIGHTING_SYSTEMS module-attribute 

WEIGHTING_SYSTEMS: Dict[str, callable] = {
    "A": weighting_system_a,
    "C": weighting_system_c,
    "Z": weighting_system_z,
}

Dictionary with available weighting systems 'A', 'C' and 'Z'.

Functions

time_averaged_sound_level 

time_averaged_sound_level(
    pressure: NDArray[float64],
    sample_frequency: float,
    averaging_time: float,
    reference_pressure: float = REFERENCE_PRESSURE,
) -> Tuple[NDArray[float64], NDArray[float64]]

Calculate time-averaged sound pressure level.

PARAMETER DESCRIPTION
pressure

Dynamic pressure.

TYPE: NDArray[float64]

sample_frequency

Sample frequency in Hz.

TYPE: float

averaging_time

Averaging time in seconds.

TYPE: float

reference_pressure

Reference pressure. Defaults to REFERENCE_PRESSURE.

TYPE: float DEFAULT: REFERENCE_PRESSURE

RETURNS DESCRIPTION
Tuple[NDArray[float64], NDArray[float64]]

Tuple containing: - Time points in seconds - Time-averaged sound pressure levels in dB
Source code in acoustic_toolbox/standards/iec_61672_1_2013.py 
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def time_averaged_sound_level(
    pressure: NDArray[np.float64],
    sample_frequency: float,
    averaging_time: float,
    reference_pressure: float = REFERENCE_PRESSURE,
) -> Tuple[NDArray[np.float64], NDArray[np.float64]]:
    """Calculate time-averaged sound pressure level.

    Args:
        pressure: Dynamic pressure.
        sample_frequency: Sample frequency in Hz.
        averaging_time: Averaging time in seconds.
        reference_pressure: Reference pressure. Defaults to REFERENCE_PRESSURE.

    Returns:
        Tuple containing:
            - Time points in seconds
            - Time-averaged sound pressure levels in dB
    """
    levels = 10.0 * np.log10(
        average(pressure**2.0, sample_frequency, averaging_time)
        / reference_pressure**2.0
    )
    times = np.arange(levels.shape[-1]) * averaging_time
    return times, levels

average 

average(
    data: NDArray[float64],
    sample_frequency: float,
    averaging_time: float,
) -> NDArray[float64]

Average the sound pressure squared.

PARAMETER DESCRIPTION
data

Energetic quantity, e.g. p².

TYPE: NDArray[float64]

sample_frequency

Sample frequency in Hz.

TYPE: float

averaging_time

Averaging time in seconds.

TYPE: float

RETURNS DESCRIPTION
NDArray[float64]

Averaged data with time weighting applied using a low-pass filter
NDArray[float64]

with one real pole at -1/τ.
Note

Because fs·ti is generally not an integer, samples are discarded. This results in a drift of samples for longer signals (e.g. 60 minutes at 44.1 kHz).

Source code in acoustic_toolbox/standards/iec_61672_1_2013.py 
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def average(
    data: NDArray[np.float64], sample_frequency: float, averaging_time: float
) -> NDArray[np.float64]:
    """Average the sound pressure squared.

    Args:
        data: Energetic quantity, e.g. p².
        sample_frequency: Sample frequency in Hz.
        averaging_time: Averaging time in seconds.

    Returns:
        Averaged data with time weighting applied using a low-pass filter
        with one real pole at -1/τ.

    Note:
        Because fs·ti is generally not an integer, samples are discarded.
        This results in a drift of samples for longer signals (e.g. 60 minutes at 44.1 kHz).
    """
    averaging_time = np.asarray(averaging_time)
    sample_frequency = np.asarray(sample_frequency)
    samples = data.shape[-1]
    n = np.floor(averaging_time * sample_frequency).astype(int)
    data = data[..., 0 : n * (samples // n)]  # Drop the tail of the signal.
    newshape = list(data.shape[0:-1])
    newshape.extend([-1, n])
    data = data.reshape(newshape)
    # data = data.reshape((-1, n))
    return data.mean(axis=-1)

time_weighted_sound_level 

time_weighted_sound_level(
    pressure: NDArray[float64],
    sample_frequency: float,
    integration_time: float,
    reference_pressure: float = REFERENCE_PRESSURE,
) -> Tuple[NDArray[float64], NDArray[float64]]

Calculate time-weighted sound pressure level.

PARAMETER DESCRIPTION
pressure

Dynamic pressure.

TYPE: NDArray[float64]

sample_frequency

Sample frequency in Hz.

TYPE: float

integration_time

Integration time in seconds.

TYPE: float

reference_pressure

Reference pressure. Defaults to REFERENCE_PRESSURE.

TYPE: float DEFAULT: REFERENCE_PRESSURE

RETURNS DESCRIPTION
Tuple[NDArray[float64], NDArray[float64]]

Tuple containing: - Time points in seconds - Time-weighted sound pressure levels in dB
Source code in acoustic_toolbox/standards/iec_61672_1_2013.py 
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def time_weighted_sound_level(
    pressure: NDArray[np.float64],
    sample_frequency: float,
    integration_time: float,
    reference_pressure: float = REFERENCE_PRESSURE,
) -> Tuple[NDArray[np.float64], NDArray[np.float64]]:
    """Calculate time-weighted sound pressure level.

    Args:
        pressure: Dynamic pressure.
        sample_frequency: Sample frequency in Hz.
        integration_time: Integration time in seconds.
        reference_pressure: Reference pressure. Defaults to REFERENCE_PRESSURE.

    Returns:
        Tuple containing:
            - Time points in seconds
            - Time-weighted sound pressure levels in dB
    """
    levels = 10.0 * np.log10(
        integrate(pressure**2.0, sample_frequency, integration_time)
        / reference_pressure**2.0
    )
    times = np.arange(levels.shape[-1]) * integration_time
    return times, levels

integrate 

integrate(
    data: NDArray[float64],
    sample_frequency: float,
    integration_time: float,
) -> NDArray[float64]

Integrate the sound pressure squared using exponential integration.

PARAMETER DESCRIPTION
data

Energetic quantity, e.g. p².

TYPE: NDArray[float64]

sample_frequency

Sample frequency in Hz.

TYPE: float

integration_time

Integration time in seconds.

TYPE: float

RETURNS DESCRIPTION
NDArray[float64]

Integrated data with time weighting applied using a low-pass filter
NDArray[float64]

with one real pole at -1/τ.
Note

Because fs·ti is generally not an integer, samples are discarded. This results in a drift of samples for longer signals (e.g. 60 minutes at 44.1 kHz).

Source code in acoustic_toolbox/standards/iec_61672_1_2013.py 
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def integrate(
    data: NDArray[np.float64], sample_frequency: float, integration_time: float
) -> NDArray[np.float64]:
    """Integrate the sound pressure squared using exponential integration.

    Args:
        data: Energetic quantity, e.g. p².
        sample_frequency: Sample frequency in Hz.
        integration_time: Integration time in seconds.

    Returns:
        Integrated data with time weighting applied using a low-pass filter
        with one real pole at -1/τ.

    Note:
        Because fs·ti is generally not an integer, samples are discarded.
        This results in a drift of samples for longer signals (e.g. 60 minutes at 44.1 kHz).
    """
    samples = data.shape[-1]
    b, a = zpk2tf([1.0], [1.0, integration_time], [1.0])
    b, a = bilinear(b, a, fs=sample_frequency)
    # b, a = bilinear([1.0], [1.0, integration_time], fs=sample_frequency) # Bilinear: Analog to Digital filter.
    n = np.floor(integration_time * sample_frequency).astype(int)
    data = data[..., 0 : n * (samples // n)]
    newshape = list(data.shape[0:-1])
    newshape.extend([-1, n])
    data = data.reshape(newshape)
    # data = data.reshape((-1, n)) # Divide in chunks over which to perform the integration.
    return (
        lfilter(b, a, data)[..., n - 1] / integration_time
    )  # Perform the integration. Select the final value of the integration.

fast 

fast(data: NDArray[float64], fs: float) -> NDArray[float64]

Apply fast (F) time-weighting.

PARAMETER DESCRIPTION
data

Energetic quantity, e.g. p².

TYPE: NDArray[float64]

fs

Sample frequency in Hz.

TYPE: float

RETURNS DESCRIPTION
NDArray[float64]

Data with FAST time-weighting applied.
See Also

integrate: Base integration function used for time-weighting.

Source code in acoustic_toolbox/standards/iec_61672_1_2013.py 
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def fast(data: NDArray[np.float64], fs: float) -> NDArray[np.float64]:
    """Apply fast (F) time-weighting.

    Args:
        data: Energetic quantity, e.g. p².
        fs: Sample frequency in Hz.

    Returns:
        Data with FAST time-weighting applied.

    See Also:
        integrate: Base integration function used for time-weighting.
    """
    return integrate(data, fs, FAST)

slow 

slow(data: NDArray[float64], fs: float) -> NDArray[float64]

Apply slow (S) time-weighting.

PARAMETER DESCRIPTION
data

Energetic quantity, e.g. p².

TYPE: NDArray[float64]

fs

Sample frequency in Hz.

TYPE: float

RETURNS DESCRIPTION
NDArray[float64]

Data with SLOW time-weighting applied.
See Also

integrate: Base integration function used for time-weighting.

Source code in acoustic_toolbox/standards/iec_61672_1_2013.py 
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def slow(data: NDArray[np.float64], fs: float) -> NDArray[np.float64]:
    """Apply slow (S) time-weighting.

    Args:
        data: Energetic quantity, e.g. p².
        fs: Sample frequency in Hz.

    Returns:
        Data with SLOW time-weighting applied.

    See Also:
        integrate: Base integration function used for time-weighting.
    """
    return integrate(data, fs, SLOW)

fast_level 

fast_level(
    data: NDArray[float64], fs: float
) -> Tuple[NDArray[float64], NDArray[float64]]

Calculate time-weighted (FAST) sound pressure level.

PARAMETER DESCRIPTION
data

Dynamic pressure.

TYPE: NDArray[float64]

fs

Sample frequency in Hz.

TYPE: float

RETURNS DESCRIPTION
Tuple[NDArray[float64], NDArray[float64]]

Tuple containing: - Time points in seconds - FAST time-weighted sound pressure levels in dB
See Also

time_weighted_sound_level: Base function for calculating time-weighted levels.

Source code in acoustic_toolbox/standards/iec_61672_1_2013.py 
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def fast_level(
    data: NDArray[np.float64], fs: float
) -> Tuple[NDArray[np.float64], NDArray[np.float64]]:
    """Calculate time-weighted (FAST) sound pressure level.

    Args:
        data: Dynamic pressure.
        fs: Sample frequency in Hz.

    Returns:
        Tuple containing:
            - Time points in seconds
            - FAST time-weighted sound pressure levels in dB

    See Also:
        time_weighted_sound_level: Base function for calculating time-weighted levels.
    """
    return time_weighted_sound_level(data, fs, FAST)

slow_level 

slow_level(
    data: NDArray[float64], fs: float
) -> Tuple[NDArray[float64], NDArray[float64]]

Calculate time-weighted (SLOW) sound pressure level.

PARAMETER DESCRIPTION
data

Dynamic pressure.

TYPE: NDArray[float64]

fs

Sample frequency in Hz.

TYPE: float

RETURNS DESCRIPTION
Tuple[NDArray[float64], NDArray[float64]]

Tuple containing: - Time points in seconds - SLOW time-weighted sound pressure levels in dB
See Also

time_weighted_sound_level: Base function for calculating time-weighted levels.

Source code in acoustic_toolbox/standards/iec_61672_1_2013.py 
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def slow_level(
    data: NDArray[np.float64], fs: float
) -> Tuple[NDArray[np.float64], NDArray[np.float64]]:
    """Calculate time-weighted (SLOW) sound pressure level.

    Args:
        data: Dynamic pressure.
        fs: Sample frequency in Hz.

    Returns:
        Tuple containing:
            - Time points in seconds
            - SLOW time-weighted sound pressure levels in dB

    See Also:
        time_weighted_sound_level: Base function for calculating time-weighted levels.
    """
    return time_weighted_sound_level(data, fs, SLOW)

weighting_function_a 

weighting_function_a(
    frequencies: NDArray[float64] | float,
) -> NDArray[float64]

Calculate A-weighting function in decibels.

PARAMETER DESCRIPTION
frequencies

Vector of frequencies at which to evaluate the weighting.

TYPE: NDArray[float64] | float

RETURNS DESCRIPTION
NDArray[float64]

Vector with A-weighting scaling factors in dB, calculated using
NDArray[float64]

equation E.6 from the standard with A₁₀₀₀ = -2 dB.
Note

Implementation of equation E.6 from the standard.

Source code in acoustic_toolbox/standards/iec_61672_1_2013.py 
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def weighting_function_a(
    frequencies: NDArray[np.float64] | float,
) -> NDArray[np.float64]:
    """Calculate A-weighting function in decibels.

    Args:
        frequencies: Vector of frequencies at which to evaluate the weighting.

    Returns:
        Vector with A-weighting scaling factors in dB, calculated using
        equation E.6 from the standard with A₁₀₀₀ = -2 dB.

    Note:
        Implementation of equation E.6 from the standard.
    """
    f = np.asarray(frequencies)
    offset = _NORMALIZATION_CONSTANTS["A"]
    f1, f2, f3, f4 = _POLE_FREQUENCIES.values()
    weighting = (
        20.0
        * np.log10(
            (f4**2.0 * f**4.0)
            / (
                (f**2.0 + f1**2.0)
                * np.sqrt(f**2.0 + f2**2.0)
                * np.sqrt(f**2.0 + f3**2.0)
                * (f**2.0 + f4**2.0)
            )
        )
        - offset
    )
    return weighting

weighting_function_c 

weighting_function_c(
    frequencies: NDArray[float64] | float,
) -> NDArray[float64]

Calculate C-weighting function in decibels.

PARAMETER DESCRIPTION
frequencies

Vector of frequencies at which to evaluate the weighting.

TYPE: NDArray[float64] | float

RETURNS DESCRIPTION
NDArray[float64]

Vector with C-weighting scaling factors in dB, calculated using
NDArray[float64]

equation E.1 from the standard with C₁₀₀₀ = -0.062 dB.
Note

Implementation of equation E.1 from the standard.

Source code in acoustic_toolbox/standards/iec_61672_1_2013.py 
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def weighting_function_c(
    frequencies: NDArray[np.float64] | float,
) -> NDArray[np.float64]:
    """Calculate C-weighting function in decibels.

    Args:
        frequencies: Vector of frequencies at which to evaluate the weighting.

    Returns:
        Vector with C-weighting scaling factors in dB, calculated using
        equation E.1 from the standard with C₁₀₀₀ = -0.062 dB.

    Note:
        Implementation of equation E.1 from the standard.
    """
    f = np.asarray(frequencies)
    offset = _NORMALIZATION_CONSTANTS["C"]
    f1, _, _, f4 = _POLE_FREQUENCIES.values()
    weighting = (
        20.0 * np.log10((f4**2.0 * f**2.0) / ((f**2.0 + f1**2.0) * (f**2.0 + f4**2.0)))
        - offset
    )
    return weighting

weighting_function_z 

weighting_function_z(
    frequencies: NDArray[float64] | float,
) -> NDArray[float64]

Calculate Z-weighting function in decibels.

PARAMETER DESCRIPTION
frequencies

Vector of frequencies at which to evaluate the weighting.

TYPE: NDArray[float64] | float

RETURNS DESCRIPTION
NDArray[float64]

Vector of zeros (Z-weighting applies no frequency weighting).
Source code in acoustic_toolbox/standards/iec_61672_1_2013.py 
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def weighting_function_z(
    frequencies: NDArray[np.float64] | float,
) -> NDArray[np.float64]:
    """Calculate Z-weighting function in decibels.

    Args:
        frequencies: Vector of frequencies at which to evaluate the weighting.

    Returns:
        Vector of zeros (Z-weighting applies no frequency weighting).
    """
    frequencies = np.asarray(frequencies)
    return np.zeros_like(frequencies)

weighting_system_a 

weighting_system_a() -> Tuple[
    NDArray[float64], NDArray[float64]
]

Get A-weighting filter as polynomial transfer function.

RETURNS DESCRIPTION
Tuple[NDArray[float64], NDArray[float64]]

Tuple containing: - Numerator coefficients of the transfer function - Denominator coefficients of the transfer function
Note

Implementation of equation E.6 from the standard.

Source code in acoustic_toolbox/standards/iec_61672_1_2013.py 
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def weighting_system_a() -> Tuple[NDArray[np.float64], NDArray[np.float64]]:
    """Get A-weighting filter as polynomial transfer function.

    Returns:
        Tuple containing:
            - Numerator coefficients of the transfer function
            - Denominator coefficients of the transfer function

    Note:
        Implementation of equation E.6 from the standard.
    """
    f1 = _POLE_FREQUENCIES[1]
    f2 = _POLE_FREQUENCIES[2]
    f3 = _POLE_FREQUENCIES[3]
    f4 = _POLE_FREQUENCIES[4]
    offset = _NORMALIZATION_CONSTANTS["A"]
    numerator = np.array(
        [(2.0 * np.pi * f4) ** 2.0 * (10 ** (-offset / 20.0)), 0.0, 0.0, 0.0, 0.0]
    )
    part1 = [1.0, 4.0 * np.pi * f4, (2.0 * np.pi * f4) ** 2.0]
    part2 = [1.0, 4.0 * np.pi * f1, (2.0 * np.pi * f1) ** 2.0]
    part3 = [1.0, 2.0 * np.pi * f3]
    part4 = [1.0, 2.0 * np.pi * f2]
    denomenator = np.convolve(np.convolve(np.convolve(part1, part2), part3), part4)
    return numerator, denomenator

weighting_system_c 

weighting_system_c() -> Tuple[
    NDArray[float64], NDArray[float64]
]

Get C-weighting filter as polynomial transfer function.

RETURNS DESCRIPTION
Tuple[NDArray[float64], NDArray[float64]]

Tuple containing: - Numerator coefficients of the transfer function - Denominator coefficients of the transfer function
Note

Implementation of equation E.1 from the standard.

Source code in acoustic_toolbox/standards/iec_61672_1_2013.py 
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def weighting_system_c() -> Tuple[NDArray[np.float64], NDArray[np.float64]]:
    """Get C-weighting filter as polynomial transfer function.

    Returns:
        Tuple containing:
            - Numerator coefficients of the transfer function
            - Denominator coefficients of the transfer function

    Note:
        Implementation of equation E.1 from the standard.
    """
    f1 = _POLE_FREQUENCIES[1]
    f4 = _POLE_FREQUENCIES[4]
    offset = _NORMALIZATION_CONSTANTS["C"]
    numerator = np.array(
        [(2.0 * np.pi * f4) ** 2.0 * (10 ** (-offset / 20.0)), 0.0, 0.0]
    )
    part1 = [1.0, 4.0 * np.pi * f4, (2.0 * np.pi * f4) ** 2.0]
    part2 = [1.0, 4.0 * np.pi * f1, (2.0 * np.pi * f1) ** 2.0]
    denomenator = np.convolve(part1, part2)
    return numerator, denomenator

weighting_system_z 

weighting_system_z() -> Tuple[list[float], list[float]]

Get Z-weighting filter as polynomial transfer function.

RETURNS DESCRIPTION
Tuple[list[float], list[float]]

Tuple containing: - [1] (numerator for unity gain) - [1] (denominator for unity gain)
Note

Z-weighting applies no frequency weighting (0.0 dB at all frequencies), therefore corresponds to multiplication by 1.

Source code in acoustic_toolbox/standards/iec_61672_1_2013.py 
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def weighting_system_z() -> Tuple[list[float], list[float]]:
    """Get Z-weighting filter as polynomial transfer function.

    Returns:
        Tuple containing:
            - [1] (numerator for unity gain)
            - [1] (denominator for unity gain)

    Note:
        Z-weighting applies no frequency weighting (0.0 dB at all frequencies),
        therefore corresponds to multiplication by 1.
    """
    numerator = [1]
    denomenator = [1]
    return numerator, denomenator