在 Python 中實現低通濾波器

import numpy as np
from scipy.signal import butter, lfilter, freqz
import matplotlib.pyplot as plt


def butter_lowpass(cutoff, fs, order=5):
    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, cutoff, fs, order=5):
    b, a = butter_lowpass(cutoff, fs, order=order)
    y = lfilter(b, a, data)
    return y


# Setting standard filter requirements.
order = 6
fs = 30.0
cutoff = 3.667

b, a = butter_lowpass(cutoff, fs, order)

# Plotting the frequency response.
w, h = freqz(b, a, worN=8000)
plt.subplot(2, 1, 1)
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("Lowpass Filter Frequency Response")
plt.xlabel("Frequency [Hz]")
plt.grid()


# Creating the data for filteration
T = 5.0  # value taken in seconds
n = int(T * fs)  # indicates total samples
t = np.linspace(0, T, n, endpoint=False)

data = (
    np.sin(1.2 * 2 * np.pi * t)
    + 1.5 * np.cos(9 * 2 * np.pi * t)
    + 0.5 * np.sin(12.0 * 2 * np.pi * t)
)

# Filtering and plotting
y = butter_lowpass_filter(data, cutoff, fs, order)

plt.subplot(2, 1, 2)
plt.plot(t, data, "b-", label="data")
plt.plot(t, y, "g-", linewidth=2, label="filtered data")
plt.xlabel("Time [sec]")
plt.grid()
plt.legend()

plt.subplots_adjust(hspace=0.35)
plt.show()