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## FILTERS (filters.py)
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## Milan Rother 2024
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# IMPORTS ===============================================================================
import numpy as np
from scipy.signal import butter, tf2ss
from math import factorial
from .lti import StateSpace
# FILTER BLOCKS =========================================================================
[docs]
class ButterworthLowpassFilter(StateSpace):
"""Direct implementation of a low pass butterworth filter block.
Follows the same structure as the 'StateSpace' block in the
'pathsim.blocks' module. The numerator and denominator of the
filter transfer function are generated and then the transfer
function is realized as a state space model.
Parameters
----------
Fc : float
corner frequency of the filter in [Hz]
n : int
filter order
"""
def __init__(self, Fc, n):
#filter parameters
self.Fc = Fc
self.n = n
#use scipy.signal for filter design for unit frequency
num, den = butter(n, 1.0, btype="low", analog=True, output="ba")
A, B, C, D = tf2ss(num, den)
#rescale to actual bandwidth and make statespace model
omega_c = 2*np.pi*self.Fc
super().__init__(omega_c*A, omega_c*B, C, D)
[docs]
class ButterworthHighpassFilter(StateSpace):
"""Direct implementation of a high pass butterworth filter block.
Follows the same structure as the 'StateSpace' block in the
'pathsim.blocks' module. The numerator and denominator of the
filter transfer function are generated and then the transfer
function is realized as a state space model.
Parameters
----------
Fc : float
corner frequency of the filter in [Hz]
n : int
filter order
"""
def __init__(self, Fc, n):
#filter parameters
self.Fc = Fc
self.n = n
#use scipy.signal for filter design for unit frequency
num, den = butter(n, 1.0, btype="high", analog=True, output="ba")
A, B, C, D = tf2ss(num, den)
#rescale to actual bandwidth and make statespace model
omega_c = 2*np.pi*self.Fc
super().__init__(omega_c*A, omega_c*B, C, D)
[docs]
class ButterworthBandpassFilter(StateSpace):
"""Direct implementation of a bandpass butterworth filter block.
Follows the same structure as the 'StateSpace' block in the
'pathsim.blocks' module. The numerator and denominator of the
filter transfer function are generated and then the transfer
function is realized as a state space model.
Parameters
----------
Fc : float
corner frequency of the filter in [Hz]
n : int
filter order
"""
def __init__(self, Fc, n):
#filter parameters
self.Fc = np.asarray(Fc)
self.n = n
if len(Fc) != 2:
raise ValueError("'ButterworthBandpassFilter' requires two corner frequencies!")
#use scipy.signal for filter design
num, den = butter(n, 2*np.pi*self.Fc, btype="bandpass", analog=True, output="ba")
#initialize parent block
super().__init__(*tf2ss(num, den))
[docs]
class ButterworthBandstopFilter(StateSpace):
"""Direct implementation of a bandstop butterworth filter block.
Follows the same structure as the 'StateSpace' block in the
'pathsim.blocks' module. The numerator and denominator of the
filter transfer function are generated and then the transfer
function is realized as a state space model.
Parameters
----------
Fc : tuple[float], list[float]
corner frequencies (left, right) of the filter in [Hz]
n : int
filter order
"""
def __init__(self, Fc, n):
#filter parameters
self.Fc = np.asarray(Fc)
self.n = n
if len(Fc) != 2:
raise ValueError("'ButterworthBandstopFilter' requires two corner frequencies!")
#use scipy.signal for filter design
num, den = butter(n, 2*np.pi*self.Fc, btype="bandstop", analog=True, output="ba")
#initialize parent block
super().__init__(*tf2ss(num, den))
[docs]
class AllpassFilter(StateSpace):
"""Direct implementation of a first order allpass filter, or a cascade
of n 1st order allpass filters
.. math::
H(s) = \\frac{s - 2\\pi f_s}{s + 2\\pi f_s}
where f_s is the frequency, where the 1st order allpass has a 90 deg phase shift.
Parameters
----------
f_s : float
frequency for 90 deg phase shift of 1st order allpass
n : int
number of cascades
"""
def __init__(self, fs, n=1):
#filter parameters
self.fs = fs
self.n = n
#1st order allpass for numerator and denominator (normalized frequency)
num = [-1, 1]
den = [1, 1]
#higher order by convolution
for _ in range(1, self.n):
num = np.convolve(num, [-1, 1])
den = np.convolve(den, [1, 1])
#create statespace model
A, B, C, D = tf2ss(num, den)
#rescale to actual frequency and make statespace model
omega_s = 2*np.pi*fs
#initialize parent block
super().__init__(omega_s*A, omega_s*B, C, D)