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filter.py
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filter.py
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# -*- coding: utf-8 -*-
"""Filtering tools"""
# Authors: Anna Padée <[email protected]>
#
# License: BSD-3-Clause
import numpy as np
from scipy.signal import butter, freqz, filtfilt
import matplotlib.pyplot as plt
def butter_lowpass(cutoff: float, fs: float, order: int = 5):
"""
Calculate parameters of a butterworth lowpass filter.
Args:
cutoff: cuttoff frequency in Hz
fs: sample frequency in Hz
order: order of the filter
Returns:
a, b (float): Numerator (b) and denominator (a) polynomial coefficients of the filter
"""
nyq = 0.5 * fs
normal_cutoff = cutoff / nyq
b, a = butter(order, normal_cutoff, btype='low', analog=False)
return b, a
def butter_lowpass_filter(data: np.ndarray, cutoff: float, fs: float, order: int = 5):
"""
Filter the data with lowpass butterworth filter
Args:
data: Array of data values; Two rows (O2Hb and HHb) for each channel
cutoff: cuttoff frequency in Hz
fs: sample frequency in Hz
order: order of the filter
Returns:
result (numpy.ndarray): 2D array of filtered data. If the input was 1D, the new shape will be (1, n_of_samples)
"""
data = np.atleast_2d(data)
result = np.empty_like(data)
b, a = butter_lowpass(cutoff, fs, order=order)
for i in range(0,len(data[:, 0])):
#filtfilt applies the same filter twice: forward and backwards, which cancels out phase distortion
# and doesn't cause delay in the signal, unlike lfilter(), which filters the same way twice
result[i, :] = filtfilt(b, a, data[i,:])
return result
def plot_lowpass_response(cutoff: float, fs: float, order: int):
"""
Plot the lowpass filter response in frequency domain
Args:
cutoff: cuttoff frequency in Hz
fs: sample frequency in Hz
order: order of the filter
Returns:
None
"""
b, a = butter_lowpass(cutoff, fs, order)
w, h = freqz(b, a)
fig = plt.figure()
fig.canvas.set_window_title('Lowpass filter response')
plt.plot(0.5*fs*w/np.pi, np.abs(h), 'b')
plt.plot(cutoff, 0.5 * np.sqrt(2), 'ko')
plt.axvline(cutoff, color='k')
plt.xlim(0, 0.5 * fs)
plt.title("Filter response")
plt.xlabel('Freq[Hz]')
plt.grid()
plt.show()
def butter_bandpass(cut_low: float, cut_high: float, fs: float, order: int = 5):
"""
Calculate parameters of a butterworth bandpass filter.
Args:
cut_low: lower cuttoff frequency in Hz
cut_high: upper cuttoff frequency in Hz
fs: sample frequency in Hz
order: order of the filter
Returns:
a, b (float): Numerator (b) and denominator (a) polynomial coefficients of the filter
"""
nyq = 0.5 * fs
b, a = butter(order, [cut_low / nyq, cut_high / nyq], btype='band')
return b, a
def butter_bandpass_filter(data: np.ndarray, cut_low: float, cut_high: float, fs: float, order: int = 5):
"""
Filter the data with lowpass butterworth filter
Args:
data: Array of data values; Two rows (O2Hb and HHb) for each channel
cut_low: lower cuttoff frequency in Hz
cut_high: upper cuttoff frequency in Hz
fs: sample frequency in Hz
order: order of the filter
Returns:
result (numpy.ndarray): 2D array of filtered data. If the input was 1D, the new shape will be (1, n_of_samples)
"""
data = np.atleast_2d(data)
result = np.empty_like(data)
b, a = butter_bandpass(cut_low, cut_high, fs, order=order)
for i in range(0, len(data[:, 0])):
# filtfilt applies the same filter twice: forward and backwards, which cancels out phase distortion
# and doesn't cause delay in the signal, unlike lfilter(), which filters the same way twice
result[i, :] = filtfilt(b, a, data[i, :])
return result
def plot_bandpass_response(cut_low: float, cut_high: float, fs: float, order: int):
"""
Plot the bandpass filter response in frequency domain
Args:
cut_low: lower cuttoff frequency in Hz
cut_high: upper cuttoff frequency in Hz
fs: sample frequency in Hz
order: order of the filter
Returns:
None
"""
b, a = butter_bandpass(cut_low, cut_high, fs, order)
w, h = freqz(b, a)
fig = plt.figure()
fig.canvas.set_window_title('Bandpass filter response')
plt.plot(0.5*fs*w/np.pi, np.abs(h), 'b')
plt.plot(cut_low, 0.5 * np.sqrt(2), 'ko')
plt.axvline(cut_low, color='k')
plt.plot(cut_high, 0.5 * np.sqrt(2), 'ko')
plt.axvline(cut_high, color='k')
plt.xlim(0, 0.5 * fs)
plt.title("Filter response")
plt.xlabel('Freq[Hz]')
plt.grid()
plt.show()
def butter_highpass(cutoff : float, fs : float, order : int = 5):
"""
Calculate parameters of a butterworth highpass filter.
Args:
cutoff: cuttoff frequency in Hz
fs: sample frequency in Hz
order: order of the filter
Returns:
a, b (float): Numerator (b) and denominator (a) polynomial coefficients of the filter
"""
nyq = 0.5 * fs
normal_cutoff = cutoff / nyq
b, a = butter(order, normal_cutoff, btype='high', analog=False)
return b, a
def butter_highpass_filter(data : np.ndarray, cutoff : float, fs : float, order : int = 5):
"""
Filter the data with highpass butterworth filter
Args:
data: Array of data values; Two rows (O2Hb and HHb) for each channel
cutoff: cuttoff frequency in Hz
fs: sample frequency in Hz
order: order of the filter
Returns:
result (numpy.ndarray): 2D array of filtered data. If the input was 1D, the new shape will be (1, n_of_samples)
"""
data = np.atleast_2d(data)
result = np.empty_like(data)
b, a = butter_highpass(cutoff, fs, order=order)
for i in range(0,len(data[:, 0])):
#filtfilt applies the same filter twice: forward and backwards, which cancels out phase distortion
# and doesn't cause delay in the signal, unlike lfilter(), which filters the same way twice
result[i, :] = filtfilt(b, a, data[i, :])
return result
def detrend(data: np.ndarray, polydeg: int = 3, downsample: int = 1):
"""
Removes trend from the data by approximating it with a polynomial.
Args:
data: Data array (channels, timepoints)
polydeg: Degree of the polynomial used for approximation
downsample: If set to n, takes only every n-th datapoint for approximation. By default, takes all datapoints.
:return: Data with the trend removed for every channel
"""
if not ("numpy.ndarray" in str(type(data))):
raise TypeError('Data must be numpy ndarray, not %s' % type(data))
nsamples = len(data[0, :])
nchannels = len(data[:, 0])
xaxis = np.array(range(0, nsamples))
result = np.zeros((nchannels, nsamples))
for i in range(0, nchannels):
coeffs = np.polyfit(xaxis[::downsample], data[i, ::downsample], deg=polydeg)
fitted = np.polyval(coeffs, xaxis)
result[i, :] = data[i, :] - fitted
return result