""" **Description**
        A complex band pass filter produces a complex exponential incident
        signal at a specified normalized frequency and adapts a forward complex
        coefficient to produce a reference signal, which estimates a component
        of interest in a primary signal.  A normalized frequency and rate of
        adaptation are specified.

        .. math::
            x_{n} = e^{\ j\ \pi\ \phi_{n}}

        .. math::
            \phi_{n+1} = \phi_{n} + f_{n}

        .. math::
            y_{n} = b_{n} x_{n}

        .. math::
            e_{n} = d_{n} - y_{n}

        .. math::
            b_{n+1} = b_{n} + \mu e_{n} x_{n}^{*}

    **Example**
        
        ::
        
            from diamondback import ComplexBandPassFilter, ComplexExponentialFilter
            import numpy

            frequency = 0.1
            x = numpy.linspace( -1.0e-4, 1.0e-4, 128 ) + frequency

            # Create a primary signal.

            d = ComplexExponentialFilter( phase = numpy.random.rand( 1 )[ 0 ] * 2.0 - 1.0 ).filter( x )

            # Create an instance.

            obj = ComplexBandPassFilter( frequency = frequency, rate = 5.0e-2 )

            # 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 - 2022 Larry Turner, Schneider Electric Industries SAS. All rights reserved.

    **Author**
        Larry Turner, Schneider Electric, Analytics & AI, 2018-01-31.
"""

from diamondback.filters.ComplexExponentialFilter import ComplexExponentialFilter
from diamondback.filters.FirFilter import FirFilter
from typing import List, Tuple, Union
import numpy
import scipy

class ComplexBandPassFilter( FirFilter ) :

    """ Complex band pass filter.
    """

    @property
    def frequency( self ) :

        """ frequency : float - relative to Nyquist in [ -1.0, 1.0 ].
        """

        return self._frequency

    @frequency.setter
    def frequency( self, frequency : float ) :

        if ( ( frequency < -1.0 ) or ( frequency > 1.0 ) ) :
            raise ValueError( f'Frequency = {frequency}' )
        self._frequency = frequency

    @property
    def rate( self ) :

        """ rate : float - in [ 0.0, 1.0 ].
        """

        return self._rate

    @rate.setter
    def rate( self, rate : float ) :

        if ( ( rate < 0.0 ) or ( rate > 1.0 ) ) :
            raise ValueError( f'Rate = {rate}' )
        self._rate = rate

    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 ( ( frequency < -1.0 ) or ( frequency > 1.0 ) ) :
            raise ValueError( f'Frequency = {frequency}' )
        if ( ( rate < 0.0 ) or ( rate > 1.0 ) ) :
            raise ValueError( f'Rate = {rate}' )
        super( ).__init__( b = numpy.array( [ numpy.finfo( float ).eps + 0j ] ), s = numpy.zeros( 1, complex ) )
        self._complexexponentialfilter = ComplexExponentialFilter( )
        self._frequency, self._rate = frequency, rate

    def filter( self, d : Union[ List, numpy.ndarray ] ) -> Tuple[ numpy.ndarray, numpy.ndarray, numpy.ndarray ] :

        """ Filters a primary signal and produces a reference signal.

            Signals are Hilbert transformed to complex as necessary.

            Arguments :
                d : Union[ List, numpy.ndarray ] - primary 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 ( not len( d ) ) :
            raise ValueError( f'D = {d}' )
        if ( not numpy.iscomplex( d ).any( ) ) :
            d = scipy.signal.hilbert( d )
        x = self._complexexponentialfilter.filter( numpy.ones( len( d ) ) * self.frequency )
        y, e, b = numpy.zeros( len( x ), complex ), numpy.zeros( len( x ), complex ), numpy.zeros( len( x ), complex )
        for ii in range( 0, len( x ) ) :
            y[ ii ] = x[ ii ] * self.b[ 0 ]
            e[ ii ] = d[ ii ] - y[ ii ]
            b[ ii ] = self.b[ 0 ]
            self.b[ 0 ] += self.rate * e[ ii ] * numpy.conjugate( x[ ii ] )
        return y, e, b
