filter1.py

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='lowpass')
    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


def butter_highpass(cutoff, fs, order=5):
    nyq = 0.5 * fs
    normal_cutoff = cutoff / nyq
    b, a = butter(order, normal_cutoff, btype='highpass')
    return b, a


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


def butter_bandpass(cutoff, fs, order=5):
    nyq = 0.5 * fs
    normal_cutoff = [c / nyq for c in cutoff]
    b, a = butter(order, normal_cutoff, btype='band',analog=False)
    return b, a


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


if __name__ == "__main__":
    order = 6
    fs = 30.0       # sample rate, Hz
    cutoff = 3.667  # desired cutoff frequency of the filter, Hz

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

    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()

    # Demonstrate the use of the filter.
    # First make some data to be filtered.
    T = 5.0         # seconds
    n = int(T * fs)  # total number of samples
    t = np.linspace(0, T, n, endpoint=False)
    # "Noisy" data.  We want to recover the 1.2 Hz signal from this.
    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)

    # Filter the data, and plot both the original and filtered signals.
    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()