Blackman

`openseize.filtering.fir.Blackman`

Bases: FIR

A callable type I FIR using a Blackman window.

A Blackman window has a wide main lobe but very low side-lobes. Thus this filter has very low ripple and strong attenuation in the pass and stop bands but at the cost of wider transition bands. This filter typically leads to overdesigned filters (i.e. large tap numbers) to reduce the transition width. Its main use is for signals in which very attenuation is needed.

Attributes:

Name	Type	Description
		see FIR Base for attributes

Window Characteristics

main lobe width (MLW) = 12 pi / len(taps)
side lobe height (SLH) = -58.2 dB
side lobe roll-off rate (SLRR) = -18 dB/octave
approximate peak error (APE) = -74 dB

Examples:

>>> bman = Blackman(fpass=300, fstop=350, fs=5000)
>>> bman.btype
'lowpass'
>>> bman = Blackman(fpass=600, fstop=400, fs=1800)
>>> bman.btype
'highpass'
>>> bman = Blackman(fpass=[400, 1000], fstop=[200, 1200], fs=4000)
>>> bman.btype
'bandpass'
>>> bman = Blackman(fpass=[200, 1200], fstop=[400, 1000], fs=5000)
>>> bman.btype
'bandstop'

Source code in openseize/filtering/fir.py

class Blackman(FIR):
    """A callable type I FIR using a Blackman window.

    A Blackman window has a wide main lobe but very low side-lobes. Thus
    this filter has very low ripple and strong attenuation in the pass and
    stop bands but at the cost of wider transition bands. This filter
    typically leads to overdesigned filters (i.e. large tap numbers) to
    reduce the transition width. Its main use is for signals in which
    very attenuation is needed.

    Attributes:
        :see FIR Base for attributes

    Window Characteristics:
        - main lobe width (MLW) = 12 pi / len(taps)
        - side lobe height (SLH) = -58.2 dB
        - side lobe roll-off rate (SLRR) = -18 dB/octave
        - approximate peak error (APE) = -74 dB

    Examples:
        >>> bman = Blackman(fpass=300, fstop=350, fs=5000)
        >>> bman.btype
        'lowpass'
        >>> bman = Blackman(fpass=600, fstop=400, fs=1800)
        >>> bman.btype
        'highpass'
        >>> bman = Blackman(fpass=[400, 1000], fstop=[200, 1200], fs=4000)
        >>> bman.btype
        'bandpass'
        >>> bman = Blackman(fpass=[200, 1200], fstop=[400, 1000], fs=5000)
        >>> bman.btype
        'bandstop'
    """

    def __init__(self,
                 fpass: Union[float, Tuple[float, float]],
                 fstop: Union[float, Tuple[float, float]],
                 fs: int
    ) -> None:
        """Initialize this Blackman windowed FIR.

        Args:
            fpass:
                The pass band edge frequency in the same units as fs OR
                a 2-el sequence of edge frequencies that are monotonically
                increasing and in [0, fs/2].
            fstop:
                The stop band edge frequency in the same units as fs OR
                a 2-el sequence of edge frequencies that are monotonically
                increasing and in [0, fs/2].
            fs:
                The sampling rate of the digital system.
        """

        # for plotting, provide a gpass calculated from the peak error
        peak_err = -74
        gpass = -20 * np.log10(1 - 10 ** (peak_err / 20))
        super().__init__(fpass, fstop, gpass=gpass, gstop=peak_err, fs=fs)

    @property
    def numtaps(self):
        """Return the number of taps to meet the transition width."""

        ntaps = int(12 / (self.width / self.nyq))
        # odd tap number to ensure group delay is integer samples
        return ntaps + 1 if ntaps % 2 == 0 else ntaps

`init(fpass, fstop, fs)`

Initialize this Blackman windowed FIR.

Parameters:

Name	Type	Description	Default
`fpass`	`Union[float, Tuple[float, float]]`	The pass band edge frequency in the same units as fs OR a 2-el sequence of edge frequencies that are monotonically increasing and in [0, fs/2].	required
`fstop`	`Union[float, Tuple[float, float]]`	The stop band edge frequency in the same units as fs OR a 2-el sequence of edge frequencies that are monotonically increasing and in [0, fs/2].	required
`fs`	`int`	The sampling rate of the digital system.	required

Source code in openseize/filtering/fir.py

def __init__(self,
             fpass: Union[float, Tuple[float, float]],
             fstop: Union[float, Tuple[float, float]],
             fs: int
) -> None:
    """Initialize this Blackman windowed FIR.

    Args:
        fpass:
            The pass band edge frequency in the same units as fs OR
            a 2-el sequence of edge frequencies that are monotonically
            increasing and in [0, fs/2].
        fstop:
            The stop band edge frequency in the same units as fs OR
            a 2-el sequence of edge frequencies that are monotonically
            increasing and in [0, fs/2].
        fs:
            The sampling rate of the digital system.
    """

    # for plotting, provide a gpass calculated from the peak error
    peak_err = -74
    gpass = -20 * np.log10(1 - 10 ** (peak_err / 20))
    super().__init__(fpass, fstop, gpass=gpass, gstop=peak_err, fs=fs)

`numtaps()` `property`

Return the number of taps to meet the transition width.

Source code in openseize/filtering/fir.py

@property
def numtaps(self):
    """Return the number of taps to meet the transition width."""

    ntaps = int(12 / (self.width / self.nyq))
    # odd tap number to ensure group delay is integer samples
    return ntaps + 1 if ntaps % 2 == 0 else ntaps

Bases and Mixins

FIR Base

Bases: abc.ABC, mixins.ViewInstance, FIRViewer

Base class for finite 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.
`nyq`	`float`	The nyquist rate of the digital system, fs/2.
`width`	`float`	The minimum transition width between the pass and stopbands.
`coeffs`	`np.ndarray`	A 1-D numpy array of filter coeffecients.

Notes

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

`btype()` `property`

Returns the string band type of this filter.

`ftype()` `property`

Returns the string name of this FIR filter.

`pass_attenuation()` `property`

Converts the max passband ripple, gpass, into a pass band attenuation in dB.

`cutoff()` `property`

Returns an ndarray of the -6 dB points of each transition band.

`call(data, chunksize, axis=-1, mode='same', **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`
`mode`	`str`	A numpy convolve mode; one of 'full', 'same', 'valid'. Full: This mode includes all points of the convolution of the filter window and data. This mode does not compensate for the delay introduced by the filter. Same: This mode (Default) returns data of the same size as the input. This mode adjust for the delay introduced by the filter. Valid: This mode returns values only when the filter and data completely overlap. The result using this mode is to shift the data (num_taps - 1) / 2 samples to the left of the input data.	`'same'`
`kwargs`		Any valid keyword argument for 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`

Blackman

openseize.filtering.fir.Blackman

__init__(fpass, fstop, fs)

numtaps() property

Bases and Mixins

FIR Base

btype() property

ftype() property

pass_attenuation() property

cutoff() property

__call__(data, chunksize, axis=-1, mode='same', **kwargs)

Viewer Mixin

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

`openseize.filtering.fir.Blackman`

`init(fpass, fstop, fs)`

`numtaps()` `property`

`btype()` `property`

`ftype()` `property`

`pass_attenuation()` `property`

`cutoff()` `property`

`call(data, chunksize, axis=-1, mode='same', **kwargs)`

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