""" **Description**
A complex frequency filter adapts and discriminates the phase of a forward
complex coefficient to produce a reference signal, which estimates a normalized
frequency of a primary signal which is normalized to unity magnitude. A
normalized frequency and rate of adaptation are specified.
.. math::
f_{n} = \\frac{\\tan^{-1}(\ b_{n}\ ) }{\pi}
.. math::
x_{n} = \\frac{d_{n}}{|\ d_{n}\ |}
.. math::
y_{n} = b_{n} x_{n-1}
.. math::
e_{n} = d_{n} - y_{n}
.. math::
b_{0} = e^{\ j\ \pi\ f_{0}}
.. math::
b_{n} = b_{n} + \mu e_{n} x_{n}^{*}
**Example**
::
from diamondback import ComplexExponentialFilter
import numpy
x = numpy.linspace( 0.0, 0.1, 128 )
# Create a primary signal.
d = ComplexExponentialFilter( 0.0 ).filter( x )
# Create an instance with frequency and rate.
obj = ComplexFrequencyFilter( frequency = 0.0, rate = 0.1 )
# Filter a primary signal.
obj.reset( d[ 0 ] )
y, e, b = obj.filter( d )
**License**
`BSD-3C. <https://github.com/larryturner/diamondback/blob/master/license>`_
© 2018 - 2021 Larry Turner, Schneider Electric Industries SAS. All rights reserved.
**Author**
Larry Turner, Schneider Electric, Analytics & AI, 2018-02-01.
**Definition**
"""
from diamondback.filters.FirFilter import FirFilter
from diamondback.interfaces.IFrequency import IFrequency
from diamondback.interfaces.IRate import IRate
import math
import numpy
import typing
[docs]class ComplexFrequencyFilter( FirFilter, IFrequency, IRate ) :
""" Complex frequency filter.
"""
@IFrequency.frequency.setter
def frequency( self, frequency : float) :
""" frequency : float - relative to Nyquist in [ -1.0, 1.0 ].
"""
IFrequency.frequency.fset( self, frequency )
self.b[ 0 ] = numpy.exp( 1j * math.pi * self.frequency )
def __init__( self, frequency : float, rate : float ) -> None :
""" Initialize.
Arguments :
frequency : float - relative to Nyquist in [ -1.0, 1.0 ).
rate : float - in [ 0.0, 1.0 ].
"""
if ( ( rate < 0.0 ) or ( rate > 1.0 ) ) :
raise ValueError( f'Rate = {rate}' )
super( ).__init__( numpy.ones( 1, complex ), numpy.ones( 1, complex ) )
self.frequency, self.rate = frequency, rate
[docs] def filter( self, d : typing.Union[ typing.List, numpy.ndarray ], x : typing.Union[ typing.List, numpy.ndarray ] = None ) -> typing.Tuple[ numpy.ndarray, numpy.ndarray, numpy.ndarray ] :
""" Filters an incident signal and produces a reference signal.
Arguments :
d : typing.Union[ typing.List, numpy.ndarray ] - primary signal.
x : typing.Union[ typing.List, numpy.ndarray ] - incident signal.
Returns :
y : numpy.ndarray - reference signal.
e : numpy.ndarray - error signal.
b : numpy.ndarray - forward coefficient.
"""
if ( ( not numpy.isscalar( d ) ) and ( not isinstance( d, numpy.ndarray ) ) ) :
d = numpy.array( list( d ) )
if ( ( len( d.shape ) != 1 ) or ( len( d ) == 0 ) or ( not isinstance( d[ 0 ], complex ) ) ) :
raise ValueError( f'D = {d}' )
x = abs( d )
x[ numpy.isclose( x, 0.0 ) ] = 1.0
x = d / x
y, e, b = numpy.zeros( len( x ) ), numpy.zeros( len( x ), complex ), numpy.zeros( len( x ), complex )
for ii in range( 0, len( x ) ) :
y[ ii ] = numpy.angle( self.b[ 0 ] ) / math.pi
e[ ii ] = x[ ii ] - self.b[ 0 ] * self.s[ 0 ]
b[ ii ] = self.b[ 0 ]
self.b[ 0 ] += self.rate * e[ ii ] * numpy.conjugate( self.s[ 0 ] )
self.s[ 0 ] = x[ ii ]
return y, e, b
[docs] def reset( self, x : complex ) -> None :
""" Modifies a state to minimize edge effects by assuming persistent
operation at a specified primary incident condition.
Arguments :
x : complex - incident signal.
"""
if ( not numpy.isscalar( x ) ) :
raise ValueError( f'X = {x}' )
if ( numpy.isclose( x, 0.0 ) ) :
self.s[ 0 ] = 1.0
else :
self.s[ 0 ] = x / abs( x )