Notch

openseize.filtering.iir.Notch

Bases: IIR

A callable second order digital Notch IIR filter.

This IIR achieves a -3 dB attenuation at the transition band edges centered on a single rejection frequency.

Attributes:

Name	Type	Description
		see IIR Base for attributes

Examples:

>>> # design a Notch filter around 60 Hz with a 8 Hz transition
>>> notch = Notch(fstop=60, width=8, fs=5000)
>>> # print the pass and stop bands
>>> notch.fpass
array([56., 64.])
>>> notch.fstop
array([60, 60])

Source code in openseize/filtering/iir.py

class Notch(IIR):
    """A callable second order digital Notch IIR filter.

    This IIR achieves a -3 dB attenuation at the transition band edges
    centered on a single rejection frequency.

    Attributes:
        : see IIR Base for attributes

    Examples:
        >>> # design a Notch filter around 60 Hz with a 8 Hz transition
        >>> notch = Notch(fstop=60, width=8, fs=5000)
        >>> # print the pass and stop bands
        >>> notch.fpass
        array([56., 64.])
        >>> notch.fstop
        array([60, 60])
    """

    def __init__(self, fstop: float, width: float, fs:float) -> None:
        """Initialize this Second Order Notch IIR.

        Args:
            fstop:
                The stop frequency at which the filter reaches maximum
                attenuation in the same units as fs.
            width:
                The width of the trasition band centered on the stop
                frequency in the same units as fs.
            fs:
                The sampling rate of the digital system.
        """

        fpass = np.array([fstop - width / 2, fstop + width / 2])
        fstop = np.array([fstop, fstop])
        self.width = width
        # gpass is 3dB, gstop is determined by width
        super().__init__(fpass, fstop, gpass=3, gstop=None, fs=fs, fmt='ba')

    @property
    def order(self):
        """Returns the order (always 2) & the 3dB frequency of this IIR."""

        return len(self.coeffs[0]) - 1, self.fstop[0] - self.width / 2

    def _build(self):
        """Designs a second order notch filter that reaches -3 dB at the
        stop band edges."""

        center = self.fstop[0]
        return sps.iirnotch(center, center / self.width, fs=self.fs)

__init__(fstop, width, fs)

Initialize this Second Order Notch IIR.

Parameters:

Name	Type	Description	Default
fstop	float	The stop frequency at which the filter reaches maximum attenuation in the same units as fs.	required
width	float	The width of the trasition band centered on the stop frequency in the same units as fs.	required
fs	float	The sampling rate of the digital system.	required

Source code in openseize/filtering/iir.py

def __init__(self, fstop: float, width: float, fs:float) -> None:
    """Initialize this Second Order Notch IIR.

    Args:
        fstop:
            The stop frequency at which the filter reaches maximum
            attenuation in the same units as fs.
        width:
            The width of the trasition band centered on the stop
            frequency in the same units as fs.
        fs:
            The sampling rate of the digital system.
    """

    fpass = np.array([fstop - width / 2, fstop + width / 2])
    fstop = np.array([fstop, fstop])
    self.width = width
    # gpass is 3dB, gstop is determined by width
    super().__init__(fpass, fstop, gpass=3, gstop=None, fs=fs, fmt='ba')

order() property

Returns the order (always 2) & the 3dB frequency of this IIR.

Source code in openseize/filtering/iir.py

@property
def order(self):
    """Returns the order (always 2) & the 3dB frequency of this IIR."""

    return len(self.coeffs[0]) - 1, self.fstop[0] - self.width / 2

Bases and Mixins

IIR Base

Bases: abc.ABC, IIRViewer, mixins.ViewInstance

Base class for infinite impulse response filters.

Attributes:

Name	Type	Description
fpass	np.ndarray	1-D numpy array of start and stop edge frequencies of this filter's passband(s).
fstop	np.ndarray	1-D numpy array of start and stop edge frequencies of this filter's stopband(s).
gpass	float	Maximum ripple in the passband(s) in dB.
gstop	float	Minimum attenuation in the stopbands in dB.
fs	int	The sampling rate of the digital system.
fmt		A scipy filter coeffecient format specification. Must be one of: 'sos': The second-order section cascade format. This format is recommended as it is more stable than 'ba'. 'ba': Transfer function format. This format is less stable but requires fewer computations compared with 'sos'. 'zpk': This format is not used and will be converted to 'sos'.
nyq	float	The nyquist rate of the digital system, fs/2.
coeffs	np.ndarray	A numpy array of filter coeffecients.

Notes

This IIR ABC defines the common and expected methods of all concrete IIR filters in the openseize.filtering.iir module. Inheritors must override abstract methods and properties of this base to be instantiable.

btype() property

Returns the string band type of this IIR filter.

ftype() property

Returns the string name of this IIR filter.

__call__(data, chunksize, axis=-1, dephase=True, zi=None, **kwargs)

Apply this filter to an ndarray or producer of ndarrays.

Parameters:

Name	Type	Description	Default
data	Union[Producer, np.ndarray]	The data to be filtered.	required
chunksize	int	The number of samples to hold in memory during filtering.	required
axis	int	The axis of data along which to apply the filter. If data is multidimensional, the filter will be independently applied along all slices of axis.	-1
dephase	bool	Removes the delay introduced by this filter by running the filter in the forward and reverse directions of data's samples.	True
zi	Optional[np.ndarray]	Initial conditions for this filter. The shape depends on the fmt attribute. For 'sos' format, zi has shape nsections x (...,2,...) where (...,2,...) has the same shape as data but with 2 along axis. For more information see lfilter_zi and sosfilt_zi in scipy's signal module. This argument is ignored if dephase is True.	None
kwargs		Keyword arguments are passed to the producer constructor.	{}

Returns:

Type	Description
Union[Producer, np.ndarray]	Filtered result with type matching input 'data' parameter.

Viewer Mixin

A collection of common plotting methods for both IIR, FIR and Parks-McClellan filters.

All filters in openseize have the ability to plot their impulse response and frequency response to a matplotlib figure called the Viewer. This mixin is inherited by specific IIR, FIR and ParksMcClellan Viewers in this file. Each of these specific viewers is inherited by the corresponding filter type (i.e. IIR, FIR, ParksMcClellan) in the openseize filtering module.

plot(size=(8, 6), gridalpha=0.3, worN=2048, rope=-100, axarr=None, show=True)

Plots the impulse and frequency response of this filter.

Parameters:

Name	Type	Description	Default
size	Tuple[int, int]	tuple The figure size to display for the plots. Default is 8 x 6.	(8, 6)
gridalpha	float	float in [0, 1] The alpha transparency of each subplots grid. Default is 0.3	0.3
worN	int	int The number of frequencies to compute the gain and phase responses over. Default is 2048 frequencies.	2048
rope	float	float For plotting, all values below this region of practical equivalence will be set to this value. Default is -100 dB. Any filter response smaller than this will be set to -100 for plotting.	-100
axarr	Optional[Sequence[plt.Axes]]	A Matplotlib axis array. An optional axis array to plot the impulse and frequency responses to. Default None means a new axis is created.	None