Source code for diamondback.transforms.PowerSpectrumTransform
""" **Description**
A power spectrum transform converts a real or complex discrete-time
incident signal to a real discrete-frequency reference signal, which
estimates a mean power density in the incident signal relative to
frequency. A forward coefficient array is specified to define a window
filter.
Singleton.
A power spectrum transform is constructed by estimating a mean power
from a collection of Fourier transforms of an incident signal, over a
sliding window defined by a forward coefficient array which defines a
window filter. An index specifies a sample interval, or a
non-overlapping stride, between successive operations.
.. math::
v_{i,k} = \\frac{1}{N}\ \sum_{n = 0}^{N-1} b_{n} x_{n+i\ I} e^{ \\frac{\ -j\ \pi\ k \ n}{N} }
.. math::
y_{k} = \\frac{1}{C}\ \sum_{i = 0}^{C-1} v_{i,k} v^{*}_{i,k}
A power spectrum transform is normalized by incident signal length and
forms a contiguous sequence corresponding to a linear and increasing
normalized frequency.
.. math::
f_{k} = -1\ + \ 2\ \\frac{k}{N}
An incident signal length is inversely proportional to a normalized
frequency resolution.
.. math::
N = \\frac{2}{R}
**Example**
::
from diamondback import ComplexExponentialFilter, PowerSpectrumTransform
import numpy
x = ComplexExponentialFilter( 0.0 ).filter( numpy.linspace( 0.12, 0.23, 1024 ) ) * numpy.random.rand( 1 )[ 0 ]
b = WindowFilter.Factory.instance( WindowFilter, 'Hann', 128 - 1 ).b
# Transform an incident signal.
y, f = PowerSpectrumTransform.transform( x, b = b, index = len( b ) // 2 )
**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, 2018-04-13.
**Definition**
"""
from diamondback.transforms.FourierTransform import FourierTransform
import numpy
import typing
[docs]class PowerSpectrumTransform( object ) :
""" Power spectrum transform.
"""
[docs] @staticmethod
def transform( x : typing.Union[ typing.List, numpy.ndarray ], b : typing.Union[ typing.List, numpy.ndarray ], index : int ) -> typing.Tuple[ numpy.ndarray, numpy.ndarray ] :
""" Transforms a real or complex discrete-time incident signal to a
real discrete-frequency reference signal.
Arguments :
x : typing.Union[ typing.List, numpy.ndarray ] - incident signal.
b : typing.Union[ typing.List, numpy.ndarray ] - forward coefficient.
index : int.
Returns :
y : numpy.ndarray - reference signal.
f : numpy.ndarray - relative to Nyquist in [ -1.0, 1.0 ).
"""
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 ) ) :
raise ValueError( f'X = {x}' )
if ( ( not numpy.isscalar( b ) ) and ( not isinstance( b, numpy.ndarray ) ) ) :
b = numpy.array( list( b ) )
if ( ( len( b.shape ) != 1 ) or ( len( b ) == 0 ) or ( numpy.isclose( b[ 1 : -1 ], 0.0 ).any( ) ) ) :
raise ValueError( f'B = {b}' )
if ( len( x ) < len( b ) ) :
raise ValueError( f'X = {x}' )
y, f = numpy.zeros( len( b ) ), None
jj = 0
for ii in range( 0, len( x ) - len( b ) + 1, index ) :
v, f = FourierTransform.transform( x[ ii : ii + len( b ) ], b )
y += abs( v * numpy.conjugate( v ) )
jj += 1
y /= jj
return y, f