""" **Description**
A complex exponential filter produces a complex exponential reference
signal from an incident signal equal to a specified normalized frequency.
A normalized phase is specified.
.. math::
x_{n} = f_{n}
.. math::
\phi_{n} = \phi_{n-1} + x_{n}
.. math::
y_{n} = e^{\ j\ \pi\ \phi_{n}}
**Example**
::
from diamondback import ComplexExponentialFilter
import numpy
# Create an instance with phase.
obj = ComplexExponentialFilter( phase = 0.0 )
# Filter an incident signal.
x = numpy.linspace( -1.0e-4, 1.0e-4, 128 ) + 0.1
y = obj.filter( x )
**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, 2018-01-31.
**Definition**
"""
from diamondback.interfaces.IPhase import IPhase
from typing import List, Union
import math
import numpy
[docs]class ComplexExponentialFilter( IPhase ) :
""" Complex exponential filter.
"""
def __init__( self, phase : float = 0.0 ) -> None :
""" Initialize.
Arguments :
phase : float - relative to pi in [ -1.0, 1.0 ].
"""
super( ).__init__( )
self.phase = phase
[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 frequency relative to Nyquist in [ -1.0, 1.0 ).
Returns :
y : numpy.ndarray - reference signal.
"""
if ( ( not numpy.isscalar( x ) ) and ( not isinstance( x, numpy.ndarray ) ) ) :
x = numpy.array( list( x ) )
if ( ( len( x.shape ) != 1 ) or ( len( x ) == 0 ) or ( abs( x ) > 1.0 ).any( ) ) :
raise ValueError( f'X = {x}' )
y = numpy.zeros( len( x ), complex )
phase = self.phase
for ii in range( 0, len( x ) ) :
y[ ii ] = numpy.exp( 1j * math.pi * phase )
phase += x[ ii ]
phase = numpy.fmod( phase, 2.0 )
if ( abs( phase ) > 1.0 ) :
phase -= numpy.sign( phase ) * 2.0
self.phase = phase
return y