Filters

Low Pass Filter

import numpy as np

import scipy.signal

import scipy.io.wavfile

import matplotlib.pyplot as plt

def lowpass(data: np.ndarray, cutoff: float, sample_rate: float, poles: int = 5):

    sos = scipy.signal.butter(poles, cutoff, 'lowpass', fs=sample_rate, output='sos')

    filtered_data = scipy.signal.sosfiltfilt(sos, data)

    return filtered_data

# Load sample data from a WAV file

sample_rate, data = scipy.io.wavfile.read('ecg.wav')

times = np.arange(len(data))/sample_rate

# Apply a 50 Hz low-pass filter to the original data

filtered = lowpass(data, 50, sample_rate)

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 3), sharex=True, sharey=True)

ax1.plot(times, data)

ax1.set_title("Original Signal")

ax1.margins(0, .1)

ax1.grid(alpha=.5, ls='--')

ax2.plot(times, filtered)

ax2.set_title("Low-Pass Filter (50 Hz)")

ax2.grid(alpha=.5, ls='--')

plt.tight_layout()

plt.show()

 

High Pass Filter

import numpy as np

import scipy.signal

import scipy.io.wavfile

import matplotlib.pyplot as plt

def highpass(data: np.ndarray, cutoff: float, sample_rate: float, poles: int = 5):

    sos = scipy.signal.butter(poles, cutoff, 'highpass', fs=sample_rate, output='sos')

    filtered_data = scipy.signal.sosfiltfilt(sos, data)

    return filtered_data

# Load sample data from a WAV file

sample_rate, data = scipy.io.wavfile.read('ecg.wav')

times = np.arange(len(data))/sample_rate

# Apply a 20 Hz high-pass filter to the original data

filtered = highpass(data, 20, sample_rate)

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 3), sharex=True, sharey=True)

ax1.plot(times, data)

ax1.set_title("Original Signal")

ax1.margins(0, .1)

ax1.grid(alpha=.5, ls='--')

ax2.plot(times, filtered)

ax2.set_title("High-Pass Filter (20 Hz)")

ax2.grid(alpha=.5, ls='--')

plt.tight_layout()

plt.show()

 

 

Band Pass Filter

import numpy as np

import scipy.signal

import scipy.io.wavfile

import matplotlib.pyplot as plt

def bandpass(data: np.ndarray, edges: list[float], sample_rate: float, poles: int = 5):

    sos = scipy.signal.butter(poles, edges, 'bandpass', fs=sample_rate, output='sos')

    filtered_data = scipy.signal.sosfiltfilt(sos, data)

    return filtered_data

# Load sample data from a WAV file

sample_rate, data = scipy.io.wavfile.read('ecg.wav')

times = np.arange(len(data))/sample_rate

# Apply a 10-50 Hz high-pass filter to the original data

filtered = bandpass(data, [10, 50], sample_rate)

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 3), sharex=True, sharey=True)

ax1.plot(times, data)

ax1.set_title("Original Signal")

ax1.margins(0, .1)

ax1.grid(alpha=.5, ls='--')

ax2.plot(times, filtered)

ax2.set_title("Band-Pass Filter (10-50 Hz)")

ax2.grid(alpha=.5, ls='--')

plt.tight_layout()

plt.show()

 

 

Low Pass Cutoff with different Frequencies

import numpy as np

import scipy.signal

import scipy.io.wavfile

import matplotlib.pyplot as plt

# Load sample data from a WAV file

sample_rate, data = scipy.io.wavfile.read('ecg.wav')

times = np.arange(len(data))/sample_rate

# Plot the original signal

plt.plot(times, data, '.-', alpha=.5, label="original signal")

# Plot the signal low-pass filtered using different cutoffs

for cutoff in [10, 20, 30, 50]:

    sos = scipy.signal.butter(5, cutoff, 'lowpass', fs=sample_rate, output='sos')

    filtered = scipy.signal.sosfiltfilt(sos, data)

    plt.plot(times, filtered, label=f"low-pass {cutoff} Hz")

plt.legend()

plt.grid(alpha=.5, ls='--')

plt.axis([0.35, 0.5, None, None])

plt.show()

 

Filter using Convolution

import numpy as np

import scipy.io.wavfile

import matplotlib.pyplot as plt

# Load sample data from a WAV file

sample_rate, data = scipy.io.wavfile.read('ecg.wav')

times = np.arange(len(data))/sample_rate

# create a Hanning kernel 1/50th of a second wide

kernel_width_seconds = 1.0/50

kernel_size_points = int(kernel_width_seconds * sample_rate)

kernel = np.hanning(kernel_size_points)

# normalize the kernel

kernel = kernel / kernel.sum()

# Create a filtered signal by convolving the kernel with the original data

filtered = np.convolve(kernel, data, mode='valid')

fig, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(10, 3))

ax1.plot(np.arange(len(kernel))/sample_rate, kernel, '.-')

ax1.set_title("Kernel (1/50 sec wide)")

ax1.grid(alpha=.5, ls='--')

ax2.plot(np.arange(len(data))/sample_rate, data)

ax2.set_title("Original Signal")

ax2.margins(0, .1)

ax2.grid(alpha=.5, ls='--')

ax3.plot(np.arange(len(filtered))/sample_rate, filtered)

ax3.set_title("Convolved Signal")

ax3.margins(0, .1)

ax3.grid(alpha=.5, ls='--')

plt.tight_layout()

plt.show()