signal_envelope.py

import numpy as np
import matplotlib.pyplot as plt
from scipy.signal import hilbert, chirp

if __name__ == "__main__":
    duration = 1.0
    fs = 400.0
    samples = int(fs * duration)
    t = np.arange(samples) / fs

    signal = chirp(t, 20.0, t[-1], 100.0)
    signal *= (1.0 + 0.5 * np.sin(2.0 * np.pi * 3.0 * t))

    analytic_signal = hilbert(signal)
    amplitude_envelope = np.abs(analytic_signal)
    instantaneous_phase = np.unwrap(np.angle(analytic_signal))
    instantaneous_frequency = (
        np.diff(instantaneous_phase) / (2.0 * np.pi) * fs)

    fig = plt.figure()
    ax0 = fig.add_subplot(211)
    ax0.plot(t, signal, label='signal')
    ax0.plot(t, amplitude_envelope, label='envelope')
    ax0.set_xlabel("time in seconds")
    ax0.legend()
    ax1 = fig.add_subplot(212)
    ax1.plot(t[1:], instantaneous_frequency)
    ax1.set_xlabel("time in seconds")
    ax1.set_ylim(0.0, 120.0)

    plt.show()