diamondback.filters package

Submodules

diamondback.filters.ComplexBandPassFilter module

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.

\[x_{n} = e^{\ j\ \pi\ \phi_{n}}\]

\[\phi_{n+1} = \phi_{n} + f_{n}\]

\[y_{n} = b_{n} x_{n}\]

\[e_{n} = d_{n} - y_{n}\]

\[b_{n+1} = b_{n} + \mu e_{n} x_{n}^{*}\]

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. © 2018 - 2024 Larry Turner, Schneider Electric Industries SAS. All rights reserved.

Author

Larry Turner, Schneider Electric, AI Hub, 2018-01-31.

class diamondback.filters.ComplexBandPassFilter.ComplexBandPassFilter(frequency: float, rate: float)

Bases: FirFilter

Complex band pass filter.

Initialize.

Arguments :

frequency : float - frequency normalized to Nyquist in [ -1.0, 1.0 ). rate : float - in [ 0.0, 1.0 ].

filter(d: list | ndarray) → Tuple[ndarray, ndarray, 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.

property frequency

property rate

diamondback.filters.ComplexExponentialFilter module

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.

\[x_{n} = f_{n}\]

\[\phi_{n} = \phi_{n-1} + x_{n}\]

\[y_{n} = e^{\ j\ \pi\ \phi_{n}}\]

Example

from diamondback import ComplexExponentialFilter
import numpy

# Create an instance.

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. © 2018 - 2024 Larry Turner, Schneider Electric Industries SAS. All rights reserved.

Author

Larry Turner, Schneider Electric, AI Hub, 2018-01-31.

class diamondback.filters.ComplexExponentialFilter.ComplexExponentialFilter(phase: float = 0.0)

Bases: object

Complex exponential filter.

Initialize.

Arguments :

phase : float - relative to pi in [ -1.0, 1.0 ].

filter(x: list | ndarray) → ndarray

Filters an incident signal and produces a reference signal.

Arguments :

x : Union[ list, numpy.ndarray ] - incident signal frequency normalized to Nyquist in [ -1.0, 1.0 ).

Returns :

y : numpy.ndarray - reference signal.

property phase

diamondback.filters.ComplexFrequencyFilter module

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.

\[f_{n} = \frac{\tan^{-1}(\ b_{n}\ ) }{\pi}\]

\[x_{n} = \frac{d_{n}}{|\ d_{n}\ |}\]

\[y_{n} = b_{n} x_{n-1}\]

\[e_{n} = d_{n} - y_{n}\]

\[b_{0} = e^{\ j\ \pi\ f_{0}}\]

\[b_{n+1} = b_{n} + \mu e_{n} x_{n}^{*}\]

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.

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. © 2018 - 2024 Larry Turner, Schneider Electric Industries SAS. All rights reserved.

Author

Larry Turner, Schneider Electric, AI Hub, 2018-02-01.

class diamondback.filters.ComplexFrequencyFilter.ComplexFrequencyFilter(frequency: float, rate: float)

Bases: FirFilter

Complex frequency filter.

Initialize.

Arguments :

frequency : float - frequency normalized to Nyquist in [ -1.0, 1.0 ). rate : float - in [ 0.0, 1.0 ].

filter(d: list | ndarray) → Tuple[ndarray, ndarray, 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.

property frequency

property rate

reset(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.

diamondback.filters.DerivativeFilter module

Description

A derivative filter realizes a discrete difference equation which approximates a discrete derivative as a function of a forward coefficient array and a state array of a specified order, consuming an incident signal and producing a reference signal. A derivative is approximated relative to a sample. A derivative is electively approximated relative to a second by multiplying a reference signal by an absolute sampling frequency raised to a derivative power.

\[y_{n} = \sum_{i = 0}^{N} b_{i} x_{n-i} = \sum_{i = 1}^{N} b_{i} s_{i,n} + b_{0} x_{n}\]

\[s_{1,n+1} = x_{n}\qquad\quad s_{i,n+1} = s_{i-1,n}\]

A frequency response is expressed as a function of a forward coefficient array.

\[H_{z} = \sum_{i = 0}^{N} b_{i} z^{-i}\]

A forward coefficient array and a state array of a specified order are defined, to satisfy specified constraints. A derivative, and order are specified.

\[y_{n} = f^{D}\ \frac{x_{n}}{D}\quad\quad\quad\quad\scriptsize{ f = 1.0 }\]

\[b_{1,1} = \scriptsize{ [ \matrix{ 1 & -1 } ] }\]

\[b_{1,2} = \scriptsize{ [ \matrix{ 1 & 0 & -1 } ]\ \frac{1}{2} }\]

\[b_{1,4} = \scriptsize{ [ \matrix{ -1 & 8 & 0 & -8 & 1 } ]\ \frac{1}{12} }\]

\[b_{2,2} = \scriptsize{ [ \matrix{ 1 & -2 & 1 } ] }\]

\[b_{2,4} = \scriptsize{ [ \matrix{ 1 & 0 & -2 & 0 & 1 } ]\ \frac{1}{4} }\]

\[b_{2,6} = \scriptsize{ [ \matrix{ -1 & 8 & 1 & -16 & 1 & 8 & -1 } ]\ \frac{1}{24} }\]

\[b_{2,8} = \scriptsize{ [ \matrix{ 1 & -16 & 64 & 16 & -130 & 16 & 64 & -16 & 1 } ]\ \frac{1}{144} }\]

\[b_{3,4} = \scriptsize{ [ \matrix{ 1 & -2 & 0 & 2 & -1 } ]\ \frac{1}{2} }\]

\[b_{3,6} = \scriptsize{ [ \matrix{ 1 & 0 & -3 & 0 & 3 & 0 & 1 } ]\ \frac{1}{8} }\]

\[b_{3,8} = \scriptsize{ [ \matrix{ -1 & 8 & 2 & -24 & 0 & 24 & -2 & -8 & 1 } ]\ \frac{1}{48} }\]

Example

from diamondback import ComplexExponentialFilter, DerivativeFilter
import numpy

# Create an instance.

obj = DerivativeFilter( derivative = 1, order = 2 )

# Filter an incident signal.

x = ComplexExponentialFilter( 0.0 ).filter( numpy.ones( 128 ) * 0.1 ).real
obj.reset( x[ 0 ] )
y = obj.filter( x )

License

BSD-3C. © 2018 - 2024 Larry Turner, Schneider Electric Industries SAS. All rights reserved.

Author

Larry Turner, Schneider Electric, AI Hub, 2018-02-06.

class diamondback.filters.DerivativeFilter.DerivativeFilter(derivative: int, order: int)

Bases: FirFilter

Derivative filter.

Initialize.

Arguments :

derivative : int - in [ 1, 3 ]. order : int.

B = {1: {1: array([1.000000, -1.000000]), 2: array([0.500000, 0.000000, -0.500000]), 4: array([-0.083333, 0.666667, 0.000000, -0.666667, 0.083333])}, 2: {2: array([1.000000, -2.000000, 1.000000]), 4: array([0.250000, 0.000000, -0.500000, 0.000000, 0.250000]), 6: array([-0.041667, 0.333333, 0.041667, -0.666667, 0.041667, 0.333333,        -0.041667]), 8: array([0.006944, -0.111111, 0.444444, 0.111111, -0.902778, 0.111111,        0.444444, -0.111111, 0.006944])}, 3: {4: array([0.500000, -1.000000, 0.000000, 1.000000, -0.500000]), 6: array([0.125000, 0.000000, -0.375000, 0.000000, 0.375000, 0.000000,        -0.125000]), 8: array([-0.020833, 0.166667, 0.041667, -0.500000, 0.000000, 0.500000,        -0.041667, -0.166667, 0.020833])}}

filter(x: list | ndarray) → ndarray

Filters an incident signal and produces a reference signal.

Arguments :

x : Union[ list, numpy.ndarray ] - incident signal.

Returns :

y : numpy.ndarray - reference signal.

diamondback.filters.FirFilter module

Description

A Finite Impulse Response (FIR) filter realizes a discrete difference equation as a function of a forward coefficient array and a state array of a specified order, consuming an incident signal and producing a reference signal.

\[y_{n} = \sum_{i = 0}^{N} b_{i,n} x_{n-i} = \sum_{i = 1}^{N} b_{i,n} s_{i,n} + b_{0,n} x_{n}\]

\[s_{1,n+1} = x_{n}\qquad\quad s_{i,n+1} = s_{i-1,n}\]

A reset may minimize edge effects at a discontinuity by assuming persistent operation at a specified incident signal condition.

\[s_{i,n} = x_{n}\]

A frequency response is expressed as a function of a forward coefficient array.

\[H_{z,n} = \sum_{i = 0}^{N} b_{i,n} z^{-i}\]

A forward coefficient array and state array of a specified order are defined to realize specified constraints. A style, frequency, order, count, complement, and gain are electively specified. Alternatively, a forward coefficient array and state array may be explicitly defined to ignore constraints.

Frequency corresponds to a -3 dB frequency response normalized relative to Nyquist.

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.

Order must even to ensure a Type I form linear phase solution.

Count is a quantity of filters of a specified order concatenated to form an aggregate frequency response in cascade form.

Complement effectively constructs a mirror image of a specified frequency response.

Example

from diamondback import FirFilter
import numpy

# Create an instance with constraints.

obj = FirFilter( style = 'Kaiser', frequency = 0.1, order = 32, count = 1 )

# Create an instance with coefficients.

obj = FirFilter( b = obj.b )

# Estimate frequency response, group delay, and roots.

y, f = obj.response( length = 8192, count = 1 )
y, f = obj.delay( length = 8192, count = 1 )
p, z = obj.roots( count = 1 )

# Filter an incident signal.

x = numpy.random.rand( 128 ) * 2.0 - 1.0
obj.reset( x[ 0 ] )
y = obj.filter( x )

License

BSD-3C. © 2018 - 2024 Larry Turner, Schneider Electric Industries SAS. All rights reserved.

Author

Larry Turner, Schneider Electric, AI Hub, 2018-01-23.

class diamondback.filters.FirFilter.FirFilter(style: str = '', frequency: float = 0.0, order: int = 0, count: int = 1, complement: bool = False, gain: float = 1.0, b: list | ndarray = [], s: list | ndarray = [])

Bases: object

Finite Impulse Response ( FIR ) filter.

Initialize.

Specify constraints including style, frequency, and order. Alternatively, a forward coefficient array may be explicitly defined to ignore constraints.

Labels should be used to avoid ambiguity between constraints and coefficients.

Arguments :

style : str - in ( ‘Blackman’, ‘Hamming’, ‘Hann’, ‘Kaiser’ ). frequency : float - frequency normalized to Nyquist in ( 0.0, 1.0 ). order : int - order per instance. count : int - instances per cascade. complement : bool - complement response. gain : float - gain. b : Union[ list, numpy.ndarray ] - forward coefficient. s : Union[ list, numpy.ndarray ] - state.

STYLE = ('Blackman', 'Hamming', 'Hann', 'Kaiser')

property b

delay(length: int = 8192, count: int = 1) → Tuple[ndarray, ndarray]

Estimates group delay and produces a reference signal.

Arguments :

length : int. count : int.

Returns :

y : numpy.ndarray - reference signal. f : numpy.ndarray - frequency normalized to Nyquist in [ -1.0, 1.0 ).

filter(x: list | ndarray) → ndarray

Filters an incident signal and produces a reference signal.

Arguments :

x : Union[ list, numpy.ndarray ] - incident signal.

Returns :

y : numpy.ndarray - reference signal.

reset(x: complex | float) → None

Modifies a state to minimize edge effects by assuming persistent operation at a specified incident signal condition.

Arguments :

x : Union[ complex, float ] - incident signal.

response(length=8192, count=1) → Tuple[ndarray, ndarray]

Estimates frequency response and produces a reference signal.

Arguments :

length : int. count : int.

Returns :

y : numpy.ndarray - reference signal. f : numpy.ndarray - frequency normalized to Nyquist in [ -1.0, 1.0 ).

roots(count=1) → Tuple[ndarray, ndarray]

Estimates roots of a frequency response in poles and zeros.

Arguments :

count : int.

Returns :

p : numpy.ndarray - poles. z : numpy.ndarray - zeros.

property s

diamondback.filters.GoertzelFilter module

Description

A Goertzel filter realizes a discrete difference equation which approximates a discrete Fourier transform evaluated at a specified normalized frequency and order, consuming an incident signal and producing a reference signal.

\[y_{n} = \sum_{i = 1}^{N} a_{i} y_{n-i} + \sum_{i = 0}^{N} b_{i} x_{n-i} = \sum_{i = 1}^{N} (\ a_{i} b_{0} + b_{i}\ ) s_{i,n} + b_{0} x_{n}\qquad a_{0} = 0\]

\[s_{1,n+1} = \sum_{i = 1}^{N} a_{i} s_{i,n} + x_{n}\qquad\quad s_{i,n+1} = s_{i-1,n}\]

\[\matrix{ a = \scriptsize{ [\ \matrix{ 0 & 2\ \cos(\ \pi\ f\ ) & -1 }\ ] } & b = \scriptsize{ [\ \matrix{ 1 & -e^{\ j\ \pi\ f\ } & 0 } }\ ] }\]

At the terminus of each window length a reference signal is evaluated to estimate a discrete Fourier transform at a specified normalized frequency.

\[H_{z} = \frac{\sum_{i = 0}^{N} b_{i} z^{-i}}{{1 - \sum_{i = 1}^{N} a_{i} z^{-i}}}\]

A Goertzel filter is normalized by incident signal length. An incident signal length is is inversely proportional to a normalized frequency resolution.

\[N = \frac{2}{R}\]

Example

from diamondback import ComplexExponentialFilter, GoertzelFilter
import numpy

b = WindowFilter( 'Hann', 128 ).b
frequency = 0.1

# Create an instance.

obj = GoertzelFilter( b = b, frequency = frequency )

# Filter an incident signal.

x = ComplexExponentialFilter( 0.0 ).filter( numpy.ones( 1024 ) * frequency ) * numpy.random.rand( 1 )[ 0 ]
y = obj.filter( x )

License

BSD-3C. © 2018 - 2024 Larry Turner, Schneider Electric Industries SAS. All rights reserved.

Author

Larry Turner, Schneider Electric, AI Hub, 2018-04-16.

class diamondback.filters.GoertzelFilter.GoertzelFilter(b: list | ndarray, frequency: float)

Bases: IirFilter

Goertzel filter.

Initialize.

Arguments :

b : Union[ list, numpy.ndarray ] - forward coefficient. frequency : float - frequency normalized to Nyquist in [ -1.0, 1.0 ].

filter(x: list | ndarray) → ndarray

Filters an incident signal and produces a reference signal.

Arguments :

x : Union[ list, numpy.ndarray ] - incident signal.

Returns :

y : numpy.ndarray - reference signal.

property frequency

diamondback.filters.IirFilter module

Description

An Infinite Impulse Response (IIR) filter realizes a discrete difference equation as a function of a recursive coefficient array, a forward coefficient array, and a state array of a specified order, consuming an incident signal and producing a reference signal.

\[y_{n} = \sum_{i = 1}^{N} a_{i,n} y_{n-i} + \sum_{i = 0}^{N} b_{i,n} x_{n-i} = \sum_{i = 1}^{N} (\ a_{i,n} b_{0,n} + b_{i,n}\ ) s_{i,n} + b_{0,n} x_{n}\qquad a_{0,n} = 0\]

\[s_{1,n+1} = \sum_{i = 1}^{N} a_{i,n} s_{i,n} + x_{n}\qquad\qquad s_{i,n+1} = s_{i-1,n}\]

A reset may minimize edge effects at a discontinuity by assuming persistent operation at a specified incident signal condition.

\[s_{i,n} = \frac{1.0 - b_{0,n}}{\sum_{i=1}^{N} a_{i,n} b_{0,n} + b_{i,n}}\ x_{n}\]

A frequency response is expressed as a function of a recursive coefficient array and a forward coefficient array.

\[H_{z,n} = \frac{\sum_{i = 0}^{N} b_{i,n} z^{-i}}{{1 - \sum_{i = 1}^{N} a_{i,n} z^{-i}}}\]

A recursive coefficient array, forward coefficient array, and state array of a specified order are defined to realize specified constraints. A style, frequency, order, count, complement, and gain are electively specified. Alternatively, a recursive coefficient array, forward coefficient array, and state array may be explicitly defined to ignore constraints.

Frequency corresponds to a -3 dB frequency response normalized relative to Nyquist.

Style is in ( ‘Bessel’, ‘Butterworth’, ‘Chebyshev’ ).

• ‘Bessel’ filters demonstrate maximally linear phase response or

  constant group delay.
• ‘Butterworth’ filters demonstrate maximally flat magnitude response.
• ‘Chebyshev’ filters demonstrate minimally low magnitude response error

  and improved rate of attenuation in a Type I form, with a maximum in

  band ripple of 0.125 dB.

Count is a quantity of filters of a specified order concatenated to form an aggregate frequency response in cascade form.

Complement effectively constructs a mirror image of a specified frequency response.

Example

from diamondback import IirFilter
import numpy

# Create an instance with constraints.

obj = IirFilter( style = 'Chebyshev', frequency = 0.1, order = 8, count = 1 )

# Create an instance with coefficients.

obj = IirFilter( a = obj.a, b = obj.b )

# Estimate frequency response, group delay, and roots.

y, f = obj.response( length = 8192, count = 1 )
y, f = obj.delay( length = 8192, count = 1 )
p, z = obj.roots( count = 1 )

# Filter an incident signal.

x = numpy.random.rand( 128 ) * 2.0 - 1.0
obj.reset( x[ 0 ] )
y = obj.filter( x )

License

BSD-3C. © 2018 - 2024 Larry Turner, Schneider Electric Industries SAS. All rights reserved.

Author

Larry Turner, Schneider Electric, AI Hub, 2018-01-23.

class diamondback.filters.IirFilter.IirFilter(style: str = '', frequency: float = 0.0, order: int = 0, count: int = 1, complement: bool = False, gain: float = 1.0, a: list | ndarray = [], b: list | ndarray = [], s: list | ndarray = [])

Bases: FirFilter

Infinite Impulse Response ( IIR ) filter.

Initialize.

Specify constraints including style, frequency, and order. Alternatively, a recursive coefficient array and forward coefficient array may be explicitly defined to ignore constraints.

Labels should be used to avoid ambiguity between constraints and coefficients.

Arguments :

style : str - in ( ‘Bessel’, ‘Butterworth’, ‘Chebyshev’ ). frequency : float - frequency normalized to Nyquist in ( 0.0, 1.0 ). order : int - order per instance. count : int - instances per cascade. complement : bool - complement response. gain : float - gain. a : Union[ list, numpy.ndarray ] - recursive coefficient. b : Union[ list, numpy.ndarray ] - forward coefficient. s : Union[ list, numpy.ndarray ] - state.

STYLE: Any = ('Bessel', 'Butterworth', 'Chebyshev')

static _evaluate(style: str, frequency: float, order: int) → Tuple[ndarray, ndarray]

Evaluates coefficients.

Arguments :

style : str - in ( ‘Bessel’, ‘Butterworth’, ‘Chebyshev’ ). frequency : float - frequency normalized to Nyquist in ( 0.0, 1.0 ). order : int.

Returns :

a : numpy.ndarray - recursive coefficient. b : numpy.ndarray - forward coefficient.

property a

delay(length: int = 8192, count: int = 1) → Tuple[ndarray, ndarray]

Estimates group delay and produces a reference signal.

Arguments :

length : int. count : int.

Returns :

y : numpy.ndarray - reference signal. f : numpy.ndarray - frequency normalized to Nyquist in [ -1.0, 1.0 ).

filter(x: list | ndarray) → ndarray

Filters an incident signal and produces a reference signal.

Arguments :

x : Union[ list, numpy.ndarray ] - incident signal.

Returns :

y : numpy.ndarray - reference signal.

reset(x: complex | float) → None

Modifies a state to minimize edge effects by assuming persistent operation at a specified incident signal condition.

Arguments :

x : Union[ complex, float ] - incident signal.

response(length=8192, count=1) → Tuple[ndarray, ndarray]

Estimates frequency response and produces a reference signal.

Arguments :

length : int. count : int.

Returns :

y : numpy.ndarray - reference signal. f : numpy.ndarray - frequency normalized to Nyquist in [ -1.0, 1.0 ).

roots(count=1) → Tuple[ndarray, ndarray]

Estimates roots of a frequency response in poles and zeros.

Arguments :

count : int.

Returns :

p : numpy.ndarray - poles. z : numpy.ndarray - zeros.

diamondback.filters.IntegralFilter module

Description

An integral filter realizes a discrete difference equation which approximates a discrete integral as a function of a recursive coefficient array, a forward coefficient array, and a state array of a specified order, consuming an incident signal and producing a reference signal. An integral is approximated relative to a sample. An integral is electively approximated relative to a second by dividing a reference signal by an absolute sampling frequency.

\[y_{n} = \sum_{i = 1}^{N} a_{i} y_{n-i} + \sum_{i = 0}^{N} b_{i} x_{n-i} = \sum_{i = 1}^{N} (\ a_{i} b_{0} + b_{i}\ ) s_{i,n} + b_{0} x_{n}\qquad a_{0} = 0\]

\[s_{1,n+1} = \sum_{i = 1}^{N} a_{i} s_{i,n} + x_{n}\qquad\quad s_{i,n+1} = s_{i-1,n}\]

A frequency response is expressed as a function of a recursive coefficient array and a forward coefficient array.

\[H_{z} = \frac{\sum_{i = 0}^{N} b_{i} z^{-i}}{{1 - \sum_{i = 1}^{N} a_{i} z^{-i}}}\]

A recursive coefficient array, forward coefficient array, and state array of a specified order are defined to satisfy specified constraints. An instance and order are specified.

\[y_{n} = \frac{1}{f}\ \sum_{i=0}^{N} x_{n}\quad\quad\quad\quad\scriptsize{ f = 1.0 }\]

\[\matrix{ a_{1,0} = \scriptsize{ [ \matrix{ 0 & 1 } ] } & b_{1,0} = \scriptsize{ [ \matrix{ 1 } ] } }\quad\quad\scriptsize{ Rectangular }\]

\[\matrix{ a_{1,1} = \scriptsize{ [ \matrix{ 0 & 1 } ] } & b_{1,1} = \scriptsize{ [ \matrix{ 1 & 1 } ]\ \frac{1}{2} } }\quad\quad\scriptsize{ Trapezoidal }\]

\[\matrix{ a_{1,2} = \scriptsize{ [ \matrix{ 0 & 1 } ] } & b_{1,2} = \scriptsize{ [ \matrix{ 1 & 4 & 1 } ]\ \frac{1}{6} } }\quad\quad\scriptsize{ Simpson\ 2 }\]

\[\matrix{ a_{1,3} = \scriptsize{ [ \matrix{ 0 & 1 } ] } & b_{1,3} = \scriptsize{ [ \matrix{ 1 & 3 & 3 & 1 } ]\ \frac{1}{8} } }\quad\quad\scriptsize{ Simpson\ 3 }\]

\[\matrix{ a_{1,4} = \scriptsize{ [ \matrix{ 0 & 1 } ] } & b_{1,4} = \scriptsize{ [ \matrix{ 7 & 32 & 12 & 32 & 7 } ]\ \frac{1}{90} } }\quad\quad\scriptsize{ Newton\ Coats }\]

Example

from diamondback import ComplexExponentialFilter, IntegralFilter
import numpy

# Create an instance.

obj = IntegralFilter( order = 2 )

# Filter an incident signal.

x = ComplexExponentialFilter( 0.0 ).filter( numpy.ones( 128 ) * 0.1 ).real
y = obj.filter( x )

License

BSD-3C. © 2018 - 2024 Larry Turner, Schneider Electric Industries SAS. All rights reserved.

Author

Larry Turner, Schneider Electric, AI Hub, 2018-02-06.

class diamondback.filters.IntegralFilter.IntegralFilter(order: int)

Bases: IirFilter

Integral filter.

Initialize.

Arguments :

order : int.

B = (array([1.000000]), array([0.500000, 0.500000]), array([0.166667, 0.666667, 0.166667]), array([0.125000, 0.375000, 0.375000, 0.125000]), array([0.077778, 0.355556, 0.133333, 0.355556, 0.077778]))

filter(x: list | ndarray) → ndarray

Filters an incident signal and produces a reference signal.

Arguments :

x : Union[ list, numpy.ndarray ] - incident signal.

Returns :

y : numpy.ndarray - reference signal.

diamondback.filters.PidFilter module

Description

A Proportional Integral Derivative (PID) filter realizes a discrete difference equation as a function of a forward coefficient array and a state array of a static order. A forward coefficient array applies a gain to proportional, integral, and derivative representations of an incident signal, producing a reference signal. An integral limit is specified, preventing integral saturation which may adversely affect control stability and latency.

\[y_{n} = b_{0}\ x_{n} + b_{1}\max(\ \min( \sum_{0}^{n}\ x_{n},\ limit\ ),\ -limit\ ) + b_{2}\ \frac{d}{dn}(\ x_{n}\ )\]

Example

from diamondback import ComplexExponentialFilter, PidFilter
import numpy

# Create an instance.

obj = PidFilter( b = numpy.array( [ 0.1, 5.0e-2, 0.0 ] ) )

# Filter an incident signal.

x = ComplexExponentialFilter( 0.0 ).filter( numpy.linspace( -1.0e-4, 1.0e-4, 128 ) * 0.1 ).real
y = obj.filter( x )

License

BSD-3C. © 2018 - 2024 Larry Turner, Schneider Electric Industries SAS. All rights reserved.

Author

Larry Turner, Schneider Electric, AI Hub, 2018-01-31.

class diamondback.filters.PidFilter.PidFilter(b: list | ndarray)

Bases: FirFilter

Proportional Integral Derivative ( PID ) filter.

Initialize.

Arguments :

b : Union[ list, numpy.ndarray ] - forward coefficient.

filter(x: list | ndarray) → ndarray

Filters an incident signal and produces a reference signal.

Arguments :

x : Union[ list, numpy.ndarray ] - incident signal.

Returns :

y : numpy.ndarray - reference signal.

property limit

diamondback.filters.PolynomialRateFilter module

Description

A polynomial rate filter produces a reference signal which approximates an incident signal evaluated at an effective frequency equal to the product of an incident sample frequency and a specified rate.

A polynomial rate filter synthesizes a sequence of polynomials which form local approximations to an incident signal, and are evaluated at indices corresponding to a specified rate to produce a reference signal, effectively modifying the sampling rate by a specified rate ratio.

A specified rate must be greater than zero, supporting decimation and interpolation.

A specified order defines the polynomial order employed to locally fit data. Unity order implies simple and efficient linear interpolation over two adjacent samples. Higher order implies a more complex polynomial fit over a sequence of four samples.

Latency compensation is not necessary, as no group delay is introduced.

Edge effects are internally mitigated by linear extension of an incident signal.

A polynomial rate filter may be the most appropriate option in applications which require fractional decimation and interpolation and benefit from minimization of edge effects due to discontinuous operation or dynamic rate.

Example

from diamondback import ComplexExponentialFilter, PolynomialRateFilter
import math
import numpy

# Create an instance.

obj = PolynomialRateFilter( rate = math.pi, order = 1 )

# Filter an incident signal.

x = ComplexExponentialFilter( 0.0 ).filter( numpy.ones( 128 ) * 0.1 ).real
y = obj.filter( x )

License

BSD-3C. © 2018 - 2024 Larry Turner, Schneider Electric Industries SAS. All rights reserved.

Author

Larry Turner, Schneider Electric, AI Hub, 2018-03-19.

class diamondback.filters.PolynomialRateFilter.PolynomialRateFilter(rate: float, order: int = 1)

Bases: object

Polynomial rate filter.

Initialize.

Arguments :

rate : float - ratio of effective frequency in [ 0.0, inf ). order : int - in [ 1 , inf ).

filter(x: list | ndarray) → ndarray

Filters an incident signal and produces a reference signal.

Arguments :

x : Union[ list, numpy.ndarray ] - incident signal.

Returns :

y : numpy.ndarray - reference signal.

property order

property rate

diamondback.filters.PolyphaseRateFilter module

Description

A polyphase rate filter produces a reference signal which approximates an incident signal evaluated at an effective frequency equal to the product of an incident sample frequency and a specified rate.

A polyphase rate filter synthesizes a polyphase filter bank with comprised of a sequence of low pass filters. Each low pass filter in a filter bank realizes a common frequency response, with a fractional sample difference in group delay. A stride is defined to be dependent upon a specified rate ratio and count. An incident signal is filtered to reduce aliasing and decimated or interpolated to produce a reference signal, effectively modifying the sampling rate by a specified rate ratio.

\[b_{k,i} = b^{M}[\ k (\ N\ +\ 1\ )\ +\ i\ ] \qquad\qquad k\ :\ [\ 0,\ K\sim 256\ )\qquad\ i\ :\ [\ 0,\ N\sim 15 \ ]\]

\[y_{n} = \sum_{i = 0}^{N} b_{k_{n},i}\ x_{n-i} = \sum_{i = 1}^{N} b_{k_{n},i}\ s_{i,n} + b_{k_{n},0}\ x_{n}\]

\[s_{1,n+1} = x_{n}\quad\quad s_{i,n+1} = s_{i-1,n}\]

A specified rate must be greater than zero, and less than or equal to the quantity of filters comprising a polyphase filter bank, supporting decimation and interpolation.

Phase dither is present for a real rate, though error is accumulated to ensure that the specified rate is realized without bias. Group delay may be addressed by latency compensation.

\[\phi_{n+1,Rate} = \phi_{n,Rate}\ +\ \frac{K}{\scriptsize{Rate}}\]

\[\phi_{n+1,Rate}\ \geq\ K\qquad\longrightarrow\qquad \phi_{n+1,Rate} = \phi_{n+1,Rate}\ -\ K\]

\[k_{n+1} = \mod(\ \lfloor{\ k_{n}\ +\ \phi_{n+1,Rate}}\rfloor,\ M\ )\]

A reset may minimize edge effects at a discontinuity by assuming persistent operation at a specified incident signal condition. Edge extension may also be applied to an incident signal.

A polyphase rate filter may be the most appropriate option in applications which require fractional decimation and interpolation and are not highly sensitive to minimization of edge effects or latency due to continuous operation.

Example

from diamondback import ComplexExponentialFilter, PolyphaseRateFilter
import math
import numpy

# Create an instance.

obj = PolyphaseRateFilter( rate = 1.0 / math.pi )

# Filter an incident signal.

x = ComplexExponentialFilter( 0.0 ).filter( numpy.ones( 128 ) * 0.1 ).real
obj.reset( x[ 0 ] )
y = obj.filter( x )

License

BSD-3C. © 2018 - 2024 Larry Turner, Schneider Electric Industries SAS. All rights reserved.

Author

Larry Turner, Schneider Electric, AI Hub, 2018-03-19.

class diamondback.filters.PolyphaseRateFilter.PolyphaseRateFilter(rate: float)

Bases: object

Polyphase rate filter.

Initialize.

Arguments :

rate : float - ratio of effective frequency in ( 0.0, b.shape[ 0 ] ].

B = array([[0.000000, 0.000000, 0.000000, ..., 0.000000, 0.000000, 0.000000],        [0.000000, 0.000000, 0.000000, ..., 0.000000, 0.000000, 0.000000],        [0.000000, 0.000000, 0.000000, ..., 0.000000, 0.000000, 0.000000],        ...,        [0.000000, 0.000000, 0.000000, ..., 0.000000, 0.000000, 0.000000],        [0.000000, 0.000000, 0.000000, ..., 0.000000, 0.000000, 0.000000],        [0.000000, 0.000000, 0.000000, ..., 0.000000, 0.000000, 0.000000]])

property b

filter(x: list | ndarray) → ndarray

Filters an incident signal and produces a reference signal.

Arguments :

x : Union[ list, numpy.ndarray ] - incident signal.

Returns :

y : numpy.ndarray - reference signal.

property rate

reset(x: float) → None

Modifies a state to minimize edge effects by assuming persistent operation at a specified incident signal condition.

Arguments :

x : float - incident signal.

property s

diamondback.filters.RankFilter module

Description

A rank filter realizes a nonlinear morphological operator consuming an incident signal, sorting, indexing, and selecting over a sliding window of a specified order, and producing a reference signal.

Simple morphological operations include dilation, which defines a rank index equal to zero, erosion, which defines a rank index equal to order, and median, which defines a rank index equal to order divided by two for even order. Compound morphological operations include close, consisting of sequential dilation and erosion, and open, consisting of sequential erosion and dilation. An order and rank are specified.

\[y_{n} = sort(\ x_{n-N+1\ :\ n}\ )[\ i\ ]\]

Example

from diamondback import RankFilter
import numpy

# Create an instance.

obj = RankFilter( rank = 4, order = 4 )

# Filter an incident signal.

x = numpy.concatenate( ( numpy.ones( 1 ), numpy.zeros( 10 ), numpy.ones( 4 ), numpy.zeros( 2 ), numpy.ones( 5 ), numpy.zeros( 6 ) ) )
obj.reset( x[ 0 ] )
y = obj.filter( x )

License

BSD-3C. © 2018 - 2024 Larry Turner, Schneider Electric Industries SAS. All rights reserved.

Author

Larry Turner, Schneider Electric, AI Hub, 2018-01-31.

class diamondback.filters.RankFilter.RankFilter(index: int, order: int)

Bases: FirFilter

Rank filter.

Initialize.

Arguments :

index : int - in [ 0, order ]. order : int.

filter(x: list | ndarray) → ndarray

Filters an incident signal and produces a reference signal.

Arguments :

x : Union[ list, numpy.ndarray ] - incident signal.

Returns :

y : numpy.ndarray - reference signal.

property index

diamondback.filters.WindowFilter module

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.

\[y_{n} = b_{n}\ x_{n}\]

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.

\[b_{n} = b_{n}\ \frac{ N }{ \sum_{0}^{N-1}\ |\ b_{n}\ |}\]

Example

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. © 2018 - 2024 Larry Turner, Schneider Electric Industries SAS. All rights reserved.

Author

Larry Turner, Schneider Electric, AI Hub, 2018-04-13.

class diamondback.filters.WindowFilter.WindowFilter(style: str, order: int, normal: bool = True)

Bases: object

Window filter.

Initialize.

Arguments :

style : str - in ( ‘Blackman’, ‘Hamming’, ‘Hann’, ‘Kaiser’ ). order : int. normal : bool.

STYLE = ('Blackman', 'Hamming', 'Hann', 'Kaiser')

property b

filter(x: list | ndarray) → ndarray

Filters an incident signal and produces a reference signal.

Arguments :

x : Union[ list, numpy.ndarray ] - incident signal.

Returns :

y : numpy.ndarray - reference signal.

Module contents

Description

Initialize.

License

BSD-3C. © 2018 - 2024 Larry Turner, Schneider Electric Industries SAS. All rights reserved.

Author

Larry Turner, Schneider Electric, AI Hub, 2018-03-22.

class diamondback.filters.ComplexBandPassFilter(frequency: float, rate: float)

Bases: FirFilter

Complex band pass filter.

Initialize.

Arguments :

frequency : float - frequency normalized to Nyquist in [ -1.0, 1.0 ). rate : float - in [ 0.0, 1.0 ].

filter(d: list | ndarray) → Tuple[ndarray, ndarray, 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.

property frequency

property rate

class diamondback.filters.ComplexExponentialFilter(phase: float = 0.0)

Bases: object

Complex exponential filter.

Initialize.

Arguments :

phase : float - relative to pi in [ -1.0, 1.0 ].

filter(x: list | ndarray) → ndarray

Filters an incident signal and produces a reference signal.

Arguments :

x : Union[ list, numpy.ndarray ] - incident signal frequency normalized to Nyquist in [ -1.0, 1.0 ).

Returns :

y : numpy.ndarray - reference signal.

property phase

class diamondback.filters.ComplexFrequencyFilter(frequency: float, rate: float)

Bases: FirFilter

Complex frequency filter.

Initialize.

Arguments :

frequency : float - frequency normalized to Nyquist in [ -1.0, 1.0 ). rate : float - in [ 0.0, 1.0 ].

filter(d: list | ndarray) → Tuple[ndarray, ndarray, 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.

property frequency

property rate

reset(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.

class diamondback.filters.DerivativeFilter(derivative: int, order: int)

Bases: FirFilter

Derivative filter.

Initialize.

Arguments :

derivative : int - in [ 1, 3 ]. order : int.

B = {1: {1: array([1.000000, -1.000000]), 2: array([0.500000, 0.000000, -0.500000]), 4: array([-0.083333, 0.666667, 0.000000, -0.666667, 0.083333])}, 2: {2: array([1.000000, -2.000000, 1.000000]), 4: array([0.250000, 0.000000, -0.500000, 0.000000, 0.250000]), 6: array([-0.041667, 0.333333, 0.041667, -0.666667, 0.041667, 0.333333,        -0.041667]), 8: array([0.006944, -0.111111, 0.444444, 0.111111, -0.902778, 0.111111,        0.444444, -0.111111, 0.006944])}, 3: {4: array([0.500000, -1.000000, 0.000000, 1.000000, -0.500000]), 6: array([0.125000, 0.000000, -0.375000, 0.000000, 0.375000, 0.000000,        -0.125000]), 8: array([-0.020833, 0.166667, 0.041667, -0.500000, 0.000000, 0.500000,        -0.041667, -0.166667, 0.020833])}}

filter(x: list | ndarray) → ndarray

Filters an incident signal and produces a reference signal.

Arguments :

x : Union[ list, numpy.ndarray ] - incident signal.

Returns :

y : numpy.ndarray - reference signal.

class diamondback.filters.FirFilter(style: str = '', frequency: float = 0.0, order: int = 0, count: int = 1, complement: bool = False, gain: float = 1.0, b: list | ndarray = [], s: list | ndarray = [])

Bases: object

Finite Impulse Response ( FIR ) filter.

Initialize.

Specify constraints including style, frequency, and order. Alternatively, a forward coefficient array may be explicitly defined to ignore constraints.

Labels should be used to avoid ambiguity between constraints and coefficients.

Arguments :

style : str - in ( ‘Blackman’, ‘Hamming’, ‘Hann’, ‘Kaiser’ ). frequency : float - frequency normalized to Nyquist in ( 0.0, 1.0 ). order : int - order per instance. count : int - instances per cascade. complement : bool - complement response. gain : float - gain. b : Union[ list, numpy.ndarray ] - forward coefficient. s : Union[ list, numpy.ndarray ] - state.

STYLE = ('Blackman', 'Hamming', 'Hann', 'Kaiser')

property b

delay(length: int = 8192, count: int = 1) → Tuple[ndarray, ndarray]

Estimates group delay and produces a reference signal.

Arguments :

length : int. count : int.

Returns :

y : numpy.ndarray - reference signal. f : numpy.ndarray - frequency normalized to Nyquist in [ -1.0, 1.0 ).

filter(x: list | ndarray) → ndarray

Filters an incident signal and produces a reference signal.

Arguments :

x : Union[ list, numpy.ndarray ] - incident signal.

Returns :

y : numpy.ndarray - reference signal.

reset(x: complex | float) → None

Modifies a state to minimize edge effects by assuming persistent operation at a specified incident signal condition.

Arguments :

x : Union[ complex, float ] - incident signal.

response(length=8192, count=1) → Tuple[ndarray, ndarray]

Estimates frequency response and produces a reference signal.

Arguments :

length : int. count : int.

Returns :

y : numpy.ndarray - reference signal. f : numpy.ndarray - frequency normalized to Nyquist in [ -1.0, 1.0 ).

roots(count=1) → Tuple[ndarray, ndarray]

Estimates roots of a frequency response in poles and zeros.

Arguments :

count : int.

Returns :

p : numpy.ndarray - poles. z : numpy.ndarray - zeros.

property s

class diamondback.filters.GoertzelFilter(b: list | ndarray, frequency: float)

Bases: IirFilter

Goertzel filter.

Initialize.

Arguments :

b : Union[ list, numpy.ndarray ] - forward coefficient. frequency : float - frequency normalized to Nyquist in [ -1.0, 1.0 ].

filter(x: list | ndarray) → ndarray

Filters an incident signal and produces a reference signal.

Arguments :

x : Union[ list, numpy.ndarray ] - incident signal.

Returns :

y : numpy.ndarray - reference signal.

property frequency

class diamondback.filters.IirFilter(style: str = '', frequency: float = 0.0, order: int = 0, count: int = 1, complement: bool = False, gain: float = 1.0, a: list | ndarray = [], b: list | ndarray = [], s: list | ndarray = [])

Bases: FirFilter

Infinite Impulse Response ( IIR ) filter.

Initialize.

Specify constraints including style, frequency, and order. Alternatively, a recursive coefficient array and forward coefficient array may be explicitly defined to ignore constraints.

Labels should be used to avoid ambiguity between constraints and coefficients.

Arguments :

style : str - in ( ‘Bessel’, ‘Butterworth’, ‘Chebyshev’ ). frequency : float - frequency normalized to Nyquist in ( 0.0, 1.0 ). order : int - order per instance. count : int - instances per cascade. complement : bool - complement response. gain : float - gain. a : Union[ list, numpy.ndarray ] - recursive coefficient. b : Union[ list, numpy.ndarray ] - forward coefficient. s : Union[ list, numpy.ndarray ] - state.

STYLE: Any = ('Bessel', 'Butterworth', 'Chebyshev')

static _evaluate(style: str, frequency: float, order: int) → Tuple[ndarray, ndarray]

Evaluates coefficients.

Arguments :

style : str - in ( ‘Bessel’, ‘Butterworth’, ‘Chebyshev’ ). frequency : float - frequency normalized to Nyquist in ( 0.0, 1.0 ). order : int.

Returns :

a : numpy.ndarray - recursive coefficient. b : numpy.ndarray - forward coefficient.

property a

delay(length: int = 8192, count: int = 1) → Tuple[ndarray, ndarray]

Estimates group delay and produces a reference signal.

Arguments :

length : int. count : int.

Returns :

y : numpy.ndarray - reference signal. f : numpy.ndarray - frequency normalized to Nyquist in [ -1.0, 1.0 ).

filter(x: list | ndarray) → ndarray

Filters an incident signal and produces a reference signal.

Arguments :

x : Union[ list, numpy.ndarray ] - incident signal.

Returns :

y : numpy.ndarray - reference signal.

reset(x: complex | float) → None

Modifies a state to minimize edge effects by assuming persistent operation at a specified incident signal condition.

Arguments :

x : Union[ complex, float ] - incident signal.

response(length=8192, count=1) → Tuple[ndarray, ndarray]

Estimates frequency response and produces a reference signal.

Arguments :

length : int. count : int.

Returns :

y : numpy.ndarray - reference signal. f : numpy.ndarray - frequency normalized to Nyquist in [ -1.0, 1.0 ).

roots(count=1) → Tuple[ndarray, ndarray]

Estimates roots of a frequency response in poles and zeros.

Arguments :

count : int.

Returns :

p : numpy.ndarray - poles. z : numpy.ndarray - zeros.

class diamondback.filters.IntegralFilter(order: int)

Bases: IirFilter

Integral filter.

Initialize.

Arguments :

order : int.

B = (array([1.000000]), array([0.500000, 0.500000]), array([0.166667, 0.666667, 0.166667]), array([0.125000, 0.375000, 0.375000, 0.125000]), array([0.077778, 0.355556, 0.133333, 0.355556, 0.077778]))

filter(x: list | ndarray) → ndarray

Filters an incident signal and produces a reference signal.

Arguments :

x : Union[ list, numpy.ndarray ] - incident signal.

Returns :

y : numpy.ndarray - reference signal.

class diamondback.filters.PidFilter(b: list | ndarray)

Bases: FirFilter

Proportional Integral Derivative ( PID ) filter.

Initialize.

Arguments :

b : Union[ list, numpy.ndarray ] - forward coefficient.

filter(x: list | ndarray) → ndarray

Filters an incident signal and produces a reference signal.

Arguments :

x : Union[ list, numpy.ndarray ] - incident signal.

Returns :

y : numpy.ndarray - reference signal.

property limit

class diamondback.filters.PolynomialRateFilter(rate: float, order: int = 1)

Bases: object

Polynomial rate filter.

Initialize.

Arguments :

rate : float - ratio of effective frequency in [ 0.0, inf ). order : int - in [ 1 , inf ).

filter(x: list | ndarray) → ndarray

Filters an incident signal and produces a reference signal.

Arguments :

x : Union[ list, numpy.ndarray ] - incident signal.

Returns :

y : numpy.ndarray - reference signal.

property order

property rate

class diamondback.filters.PolyphaseRateFilter(rate: float)

Bases: object

Polyphase rate filter.

Initialize.

Arguments :

rate : float - ratio of effective frequency in ( 0.0, b.shape[ 0 ] ].

B = array([[0.000000, 0.000000, 0.000000, ..., 0.000000, 0.000000, 0.000000],        [0.000000, 0.000000, 0.000000, ..., 0.000000, 0.000000, 0.000000],        [0.000000, 0.000000, 0.000000, ..., 0.000000, 0.000000, 0.000000],        ...,        [0.000000, 0.000000, 0.000000, ..., 0.000000, 0.000000, 0.000000],        [0.000000, 0.000000, 0.000000, ..., 0.000000, 0.000000, 0.000000],        [0.000000, 0.000000, 0.000000, ..., 0.000000, 0.000000, 0.000000]])

property b

filter(x: list | ndarray) → ndarray

Filters an incident signal and produces a reference signal.

Arguments :

x : Union[ list, numpy.ndarray ] - incident signal.

Returns :

y : numpy.ndarray - reference signal.

property rate

reset(x: float) → None

Modifies a state to minimize edge effects by assuming persistent operation at a specified incident signal condition.

Arguments :

x : float - incident signal.

property s

class diamondback.filters.RankFilter(index: int, order: int)

Bases: FirFilter

Rank filter.

Initialize.

Arguments :

index : int - in [ 0, order ]. order : int.

filter(x: list | ndarray) → ndarray

Filters an incident signal and produces a reference signal.

Arguments :

x : Union[ list, numpy.ndarray ] - incident signal.

Returns :

y : numpy.ndarray - reference signal.

property index

class diamondback.filters.WindowFilter(style: str, order: int, normal: bool = True)

Bases: object

Window filter.

Initialize.

Arguments :

style : str - in ( ‘Blackman’, ‘Hamming’, ‘Hann’, ‘Kaiser’ ). order : int. normal : bool.

STYLE = ('Blackman', 'Hamming', 'Hann', 'Kaiser')

property b

filter(x: list | ndarray) → ndarray

Filters an incident signal and produces a reference signal.

Arguments :

x : Union[ list, numpy.ndarray ] - incident signal.

Returns :

y : numpy.ndarray - reference signal.