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Sep 5th, 2020
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  1. # -*- coding: utf-8 -*-
  2. import numpy as np
  3. import matplotlib.pyplot as plt
  4.  
  5. #%%##########################################################################
  6. def _consts(sigma):
  7.     cs = (1 + np.exp(-sigma ** 2) - 2 * np.exp(-.75 * sigma ** 2)) ** (-.5)
  8.     ks = np.exp(-.5 * sigma ** 2)
  9.     return cs, ks
  10.  
  11. def morlet(N, sigma=5):
  12.     cs, ks = _consts(sigma)
  13.     n = np.linspace(-8, 8, N)
  14.     return np.exp(-.5 * n ** 2) * (np.exp(1j * sigma * n) - ks
  15.                                    ) * cs * np.pi ** (-.25)
  16.  
  17. def morlet_fourier(N, sigma):
  18.     cs, ks = _consts(sigma)
  19.     k = np.linspace(0, N - 1, N)
  20.     return (np.exp(-.5 * (sigma - k) ** 2) - ks * np.exp(-.5 * k ** 2)
  21.             ) * cs * np.pi ** (-.25)
  22.  
  23. def plot(x, complex=False):
  24.     plt.plot(x)
  25.     if complex:
  26.         plt.plot(x.imag)
  27.         plt.legend(['real', 'imag'], fontsize=14)
  28.     plt.show()
  29. #%%##########################################################################
  30. N, sigma = 256, 5
  31. morl     = morlet(N, sigma)
  32. morl_f   = morlet_fourier(N, sigma)
  33. morl_fft = np.fft.fft(morl)
  34. #%%##########################################################################
  35. plot(morl, complex=True)
  36. plot(morl_f)
  37. plot(morl_fft, complex=True)
  38. plot(np.abs(morl_fft))
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