""" **Description**
A window filter realizes a discrete difference equation as a function
of a forward coefficient array of a specified order, consuming an
incident signal and producing a reference signal.
.. math::
y_{n} = b_{n}\\ x_{n}
A forward coefficient array of a specified order is defined. A
style, order, and normalization are specified.
Style is in ( 'Blackman', 'Hamming', 'Hann', 'Kaiser' ).
* | 'Blackman' filters demonstrate low resolution and spectral leakage
| with improved rate of attenuation.
* | 'Hamming' filters demonstrate minimal nearest side lobe magnitude
| response.
* | 'Hann' filters demonstrate high resolution and spectral leakage.
* | 'Kaiser' filters demonstrate flexible resolution and spectral
| leakage dependent upon a beta value of a Bessel function of the
| first kind, with beta equal to 7.0.
Normal condition scales a forward coefficient array to electively
compensate for energy loss.
.. math::
b_{n} = b_{n}\\ \\frac{ N }{ \\sum_{0}^{N-1}\\ |\\ b_{n}\\ |}
**Example**
.. code-block:: python
from diamondback import ComplexExponentialFilter, WindowFilter
import numpy
# Create an instance.
obj = WindowFilter( style = 'Hann', order = 15, normal = True )
# Filter an incident signal.
x = ComplexExponentialFilter( 0.0 ).filter( numpy.ones( len( obj.b ) ) * 0.1 ).real
y = obj.filter( x )
**License**
`BSD-3C. <https://github.com/larryturner/diamondback/blob/master/license>`_
© 2018 - 2024 Larry Turner, Schneider Electric Industries SAS. All rights reserved.
**Author**
Larry Turner, Schneider Electric, AI Hub, 2018-04-13.
"""
from typing import Union
import numpy
import scipy.signal
[docs]
class WindowFilter( object ) :
""" Window filter.
"""
STYLE = ( 'Blackman', 'Hamming', 'Hann', 'Kaiser' )
@property
def b( self ) :
return self._b
def __init__( self, style : str, order : int, normal : bool = True ) -> None :
""" Initialize.
Arguments :
style : str - in ( 'Blackman', 'Hamming', 'Hann', 'Kaiser' ).
order : int.
normal : bool.
"""
style = style.title( )
if ( style not in WindowFilter.STYLE ) :
raise ValueError( f'style = {style} Expected Style in {WindowFilter.STYLE}' )
if ( order < 0 ) :
raise ValueError( f'Order = {order} Expected Order in [ 0, inf )' )
if ( style == 'Kaiser' ) :
window = ( style.lower( ), 7.0 )
else :
window = style.lower( ) # type: ignore
super( ).__init__( )
b = scipy.signal.get_window( window, order + 1, False )
if ( normal ) :
b *= ( order + 1 ) / sum( abs( b ) )
self._b = numpy.array( b )
[docs]
def filter( self, x : Union[ list, numpy.ndarray ] ) -> numpy.ndarray :
""" Filters an incident signal and produces a reference signal.
Arguments :
x : Union[ list, numpy.ndarray ] - incident signal.
Returns :
y : numpy.ndarray - reference signal.
"""
if ( not isinstance( x, numpy.ndarray ) ) :
x = numpy.array( list( x ) )
if ( ( len( x.shape ) != 1 ) or ( len( x ) != len( self.b ) ) ) :
raise ValueError( f'X = {x}' )
return self.b * x