IEC 61260-1:2014

IEC 61260-1:2014 specifies performance requirements for analogue, sampled-data, and digital implementations of band-pass filters.

FUNCTION	DESCRIPTION
`exact_center_frequency`	Calculate exact center frequencies for given band indices
`lower_frequency`	Calculate lower band-edge frequencies
`upper_frequency`	Calculate upper band-edge frequencies
`index_of_frequency`	Calculate the band index for a given frequency
`nominal_center_frequency`	Calculate nominal center frequencies

Constants

NOMINAL_OCTAVE_CENTER_FREQUENCIES: Nominal octave center frequencies
NOMINAL_THIRD_OCTAVE_CENTER_FREQUENCIES: Nominal third-octave center frequencies
REFERENCE_FREQUENCY: Reference frequency
OCTAVE_FREQUENCY_RATIO: Octave frequency ratio

Attributes

NOMINAL_OCTAVE_CENTER_FREQUENCIES `module-attribute`

NOMINAL_OCTAVE_CENTER_FREQUENCIES = array(
    [
        31.5,
        63.0,
        125.0,
        250.0,
        500.0,
        1000.0,
        2000.0,
        4000.0,
        8000.0,
        16000.0,
    ]
)

Nominal octave center frequencies.

NOMINAL_THIRD_OCTAVE_CENTER_FREQUENCIES `module-attribute`

NOMINAL_THIRD_OCTAVE_CENTER_FREQUENCIES = array(
    [
        25.0,
        31.5,
        40.0,
        50.0,
        63.0,
        80.0,
        100.0,
        125.0,
        160.0,
        200.0,
        250.0,
        315.0,
        400.0,
        500.0,
        630.0,
        800.0,
        1000.0,
        1250.0,
        1600.0,
        2000.0,
        2500.0,
        3150.0,
        4000.0,
        5000.0,
        6300.0,
        8000.0,
        10000.0,
        12500.0,
        16000.0,
        20000.0,
    ]
)

Nominal third-octave center frequencies in the audio range.

REFERENCE_FREQUENCY `module-attribute`

REFERENCE_FREQUENCY = 1000.0

Reference frequency.

OCTAVE_FREQUENCY_RATIO `module-attribute`

OCTAVE_FREQUENCY_RATIO = 10.0 ** (3.0 / 10.0)

Octave frequency ratio $G$.

See equation 1.

nominal_center_frequency `module-attribute`

nominal_center_frequency = vectorize(
    _nominal_center_frequency
)

Vectorized function to calculate nominal center frequencies.

PARAMETER	DESCRIPTION
`center`	Exact center frequency.
`fraction`	Band designator or fraction.

RETURNS	DESCRIPTION
	float or ndarray: Nominal center frequencies calculated according to standard.

Functions

exact_center_frequency

exact_center_frequency(
    x,
    fraction=1,
    ref=REFERENCE_FREQUENCY,
    G=OCTAVE_FREQUENCY_RATIO,
) -> float | ndarray

Center frequencies $f_m$ for band indices $x$. See equation 2 and 3.

The center frequencies are given by $$ f_m = f_r G^{x/b} $$

In case the bandwidth designator $b$ is an even number, the center frequencies are given by $$ f_m = f_r G^{(2x+1)/2b} $$

See equation 2 and 3 of the standard.

PARAMETER	DESCRIPTION
`x`	Band index $x$.
`fraction`	Bandwidth designator $b$. For example, for ⅓-octave filter $b=3$. Defaults to 1. DEFAULT: `1`
`ref`	Reference center frequency $f_r$. DEFAULT: `REFERENCE_FREQUENCY`
`G`	Octave frequency ratio $G$. DEFAULT: `OCTAVE_FREQUENCY_RATIO`

RETURNS	DESCRIPTION
`float \| ndarray`	Center frequencies $f_m$ calculated according to equations 2 and 3.

Source code in acoustic_toolbox/standards/iec_61260_1_2014.py

def exact_center_frequency(
    x, fraction=1, ref=REFERENCE_FREQUENCY, G=OCTAVE_FREQUENCY_RATIO
) -> float | np.ndarray:
    r"""Center frequencies $f_m$ for band indices $x$. See equation 2 and 3.

    The center frequencies are given by
    $$
    f_m = f_r G^{x/b}
    $$

    In case the bandwidth designator $b$ is an even number, the center frequencies are given by
    $$
    f_m = f_r G^{(2x+1)/2b}
    $$

    See equation 2 and 3 of the standard.

    Args:
        x: Band index $x$.
        fraction: Bandwidth designator $b$. For example, for 1/3-octave filter $b=3$. Defaults to 1.
        ref: Reference center frequency $f_r$.
        G: Octave frequency ratio $G$.

    Returns:
        Center frequencies $f_m$ calculated according to equations 2 and 3.
    """
    fraction = np.asarray(fraction)
    uneven = (fraction % 2).astype("bool")
    return ref * G ** ((2.0 * x + 1.0) / (2.0 * fraction)) * np.logical_not(
        uneven
    ) + uneven * ref * G ** (x / fraction)

lower_frequency

lower_frequency(
    center: float | ndarray,
    fraction=1,
    G=OCTAVE_FREQUENCY_RATIO,
) -> float | ndarray

Lower band-edge frequencies. See equation 4.

The lower band-edge frequencies are given by $$ f_1 = f_m G^{-½b} $$

See equation 4 of the standard.

PARAMETER	DESCRIPTION
`center`	Center frequencies $f_m$. TYPE: `float \| ndarray`
`fraction`	Bandwidth designator $b$. DEFAULT: `1`
`G`	Octave frequency ratio $G$. DEFAULT: `OCTAVE_FREQUENCY_RATIO`

RETURNS	DESCRIPTION
`float \| ndarray`	Lower band-edge frequencies $f_1$

Source code in acoustic_toolbox/standards/iec_61260_1_2014.py

def lower_frequency(
    center: float | np.ndarray, fraction=1, G=OCTAVE_FREQUENCY_RATIO
) -> float | np.ndarray:
    """Lower band-edge frequencies. See equation 4.

    The lower band-edge frequencies are given by
    $$
    f_1 = f_m G^{-1/2b}
    $$

    See equation 4 of the standard.

    Args:
        center: Center frequencies $f_m$.
        fraction: Bandwidth designator $b$.
        G: Octave frequency ratio $G$.

    Returns:
        Lower band-edge frequencies $f_1$
    """
    return center * G ** (-1.0 / (2.0 * fraction))

upper_frequency

upper_frequency(
    center: float | ndarray,
    fraction=1,
    G=OCTAVE_FREQUENCY_RATIO,
) -> float | ndarray

Upper band-edge frequencies. See equation 5.

The upper band-edge frequencies are given by $$ f_2 = f_m G^{+½b} $$

See equation 5 of the standard.

PARAMETER	DESCRIPTION
`center`	Center frequencies $f_m$. TYPE: `float \| ndarray`
`fraction`	Bandwidth designator $b$. DEFAULT: `1`
`G`	Octave frequency ratio $G$. DEFAULT: `OCTAVE_FREQUENCY_RATIO`

RETURNS	DESCRIPTION
`float \| ndarray`	Upper band-edge frequencies $f_2$.

Source code in acoustic_toolbox/standards/iec_61260_1_2014.py

def upper_frequency(
    center: float | np.ndarray, fraction=1, G=OCTAVE_FREQUENCY_RATIO
) -> float | np.ndarray:
    """Upper band-edge frequencies. See equation 5.

    The upper band-edge frequencies are given by
    $$
    f_2 = f_m G^{+1/2b}
    $$

    See equation 5 of the standard.

    Args:
        center: Center frequencies $f_m$.
        fraction: Bandwidth designator $b$.
        G: Octave frequency ratio $G$.

    Returns:
        Upper band-edge frequencies $f_2$.
    """
    return center * G ** (+1.0 / (2.0 * fraction))

index_of_frequency

index_of_frequency(
    frequency,
    fraction=1,
    ref=REFERENCE_FREQUENCY,
    G=OCTAVE_FREQUENCY_RATIO,
) -> int | ndarray

Calculate the band index for a given frequency.

The index of the center frequency is given by

\[ x = \text{round}\left(b \frac{\log(f/f_r)}{\log(G)}\right) \]

See equation 6 of the standard.

Note

This equation is not part of the standard. However, it follows from exact_center_frequency.

PARAMETER	DESCRIPTION
`frequency`	Frequencies $f$
`fraction`	Bandwidth designator $b$. DEFAULT: `1`
`ref`	Reference frequency. DEFAULT: `REFERENCE_FREQUENCY`
`G`	Octave frequency ratio $G$. DEFAULT: `OCTAVE_FREQUENCY_RATIO`

RETURNS	DESCRIPTION
`int \| ndarray`	Band indices $x$

Source code in acoustic_toolbox/standards/iec_61260_1_2014.py

def index_of_frequency(
    frequency, fraction=1, ref=REFERENCE_FREQUENCY, G=OCTAVE_FREQUENCY_RATIO
) -> int | np.ndarray:
    r"""Calculate the band index for a given frequency.

    The index of the center frequency is given by

    $$
    x = \text{round}\left(b \frac{\log(f/f_r)}{\log(G)}\right)
    $$

    See equation 6 of the standard.

    Note:
        This equation is not part of the standard.
        However, it follows from [`exact_center_frequency`](acoustic_toolbox.standards.iec_61260_1_2014.exact_center_frequency).

    Args:
        frequency: Frequencies $f$
        fraction: Bandwidth designator $b$.
        ref: Reference frequency.
        G: Octave frequency ratio $G$.

    Returns:
        Band indices $x$
    """
    fraction = np.asarray(fraction)
    uneven = (fraction % 2).astype("bool")
    return (
        np.round((2.0 * fraction * np.log(frequency / ref) / np.log(G) - 1.0))
        / 2.0
        * np.logical_not(uneven)
        + uneven
        * np.round(fraction * np.log(frequency / ref) / np.log(G)).astype("int16")
    ).astype("int16")

:::

PARAMETER	DESCRIPTION
`x`	Band index \(x\).
`fraction`	Bandwidth designator \(b\). For example, for ⅓-octave filter \(b=3\). Defaults to 1. DEFAULT: `1`
`ref`	Reference center frequency \(f_r\). DEFAULT: `REFERENCE_FREQUENCY`
`G`	Octave frequency ratio \(G\). DEFAULT: `OCTAVE_FREQUENCY_RATIO`

PARAMETER	DESCRIPTION
`center`	Center frequencies \(f_m\). TYPE: `float \| ndarray`
`fraction`	Bandwidth designator \(b\). DEFAULT: `1`
`G`	Octave frequency ratio \(G\). DEFAULT: `OCTAVE_FREQUENCY_RATIO`

PARAMETER	DESCRIPTION
`frequency`	Frequencies \(f\)
`fraction`	Bandwidth designator \(b\). DEFAULT: `1`
`ref`	Reference frequency. DEFAULT: `REFERENCE_FREQUENCY`
`G`	Octave frequency ratio \(G\). DEFAULT: `OCTAVE_FREQUENCY_RATIO`

IEC 61260-1:2014

Attributes

NOMINAL_OCTAVE_CENTER_FREQUENCIES module-attribute

NOMINAL_THIRD_OCTAVE_CENTER_FREQUENCIES module-attribute

REFERENCE_FREQUENCY module-attribute

OCTAVE_FREQUENCY_RATIO module-attribute

nominal_center_frequency module-attribute

Functions

exact_center_frequency

lower_frequency

upper_frequency

index_of_frequency

NOMINAL_OCTAVE_CENTER_FREQUENCIES `module-attribute`

NOMINAL_THIRD_OCTAVE_CENTER_FREQUENCIES `module-attribute`

REFERENCE_FREQUENCY `module-attribute`

OCTAVE_FREQUENCY_RATIO `module-attribute`

nominal_center_frequency `module-attribute`