signal_process.py

#### Butterworth bandpass filter
# https://scipy-cookbook.readthedocs.io/items/ButterworthBandpass.html
from scipy.signal import butter, lfilter


def butter_lowpass(lowcut, fs, order=5):
    nyq = 0.5 * fs
    low = lowcut / nyq
    b, a = butter(order, [low], btype='lowpass')
    return b, a

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


def butter_highpass(highcut, fs, order=5):
    nyq = 0.5 * fs
    high = highcut / nyq
    b, a = butter(order, [high], btype='highpass')
    return b, a

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


def butter_bandpass(lowcut, highcut, fs, order=5):
    nyq = 0.5 * fs
    low = lowcut / nyq
    high = highcut / nyq
    b, a = butter(order, [low, high], btype='bandpass')
    return b, a


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


def run():
    import numpy as np
    import matplotlib.pyplot as plt
    from scipy.signal import freqz

    # Sample rate and desired cutoff frequencies (in Hz).
    fs = 5000.0
    lowcut = 500.0
    highcut = 1250.0

#     # Plot the frequency response for a few different orders.
#     plt.figure(1)
#     plt.clf()
#     for order in [3, 6, 9]:
#         b, a = butter_bandpass(lowcut, highcut, fs, order=order)
#         w, h = freqz(b, a, worN=2000)
#         plt.plot((fs * 0.5 / np.pi) * w, abs(h), label="order = %d" % order)

#     plt.plot([0, 0.5 * fs], [np.sqrt(0.5), np.sqrt(0.5)],
#              '--', label='sqrt(0.5)')
#     plt.xlabel('Frequency (Hz)')
#     plt.ylabel('Gain')
#     plt.grid(True)
#     plt.legend(loc='best')

    # Filter a noisy signal.
    T = 0.05
    nsamples = T * fs
    t = np.linspace(0, T, nsamples, endpoint=False)
    a = 0.02
    f0 = 600.0
    x = 0.1 * np.sin(2 * np.pi * 1.2 * np.sqrt(t))
    x += 0.01 * np.cos(2 * np.pi * 312 * t + 0.1)
    x += a * np.cos(2 * np.pi * f0 * t + .11)
    x += 0.03 * np.cos(2 * np.pi * 2000 * t)
    plt.figure(2)
    plt.clf()
    plt.plot(t, x, label='Noisy signal')

    y = butter_bandpass_filter(x, lowcut, highcut, fs, order=6)
    plt.plot(t, y, label='Filtered signal (%g Hz)' % f0)
    plt.xlabel('time (seconds)')
    plt.hlines([-a, a], 0, T, linestyles='--')
    plt.grid(True)
    plt.axis('tight')
    plt.legend(loc='upper left')

    plt.show()