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a guest Jul 28th, 2017 169 Never
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  1. import numpy as np
  2. import matplotlib.pyplot as plt
  3.  
  4. """generate signal"""
  5. oversampling_factor = 5.0  # when initial Fs = 1600 - interpolate with (1600 * oversampling_factor)
  6. Fs = 1000.0  # sampling frequency
  7. n = 500.0
  8. x = np.arange(n)
  9. y_time = [np.random.randn() for item in range(0, int(n))]  # create white noise
  10.  
  11. """interpolate"""
  12. x_interpolated = np.arange(0.5, n, 1.0)  # only shifted
  13. y_interpolated1 = np.interp(x_interpolated, x, y_time)
  14. x_interpolated2 = np.arange(0.0, n, 1.0/oversampling_factor)  # oversampled
  15. y_interpolated2 = np.interp(x_interpolated2, x, y_time)
  16.  
  17. "FFT"
  18. y_freq = np.abs(np.fft.rfft(y_time)) / len(y_time)  # original signal
  19. y_freq_shifted = np.abs(np.fft.rfft(y_interpolated1)) / len(y_interpolated1)  # shifted signal
  20. y_freq_oversampled = np.abs(np.fft.rfft(y_interpolated2)) / len(y_interpolated2)  # oversampled signal
  21.  
  22. x_freq = np.fft.rfftfreq(len(y_time), d=(1.0 / Fs))
  23. x_freq_shifted = np.fft.rfftfreq(len(y_interpolated1), d=(1.0 / Fs))
  24. x_freq_oversampled = np.fft.rfftfreq(len(y_interpolated2), d=(1.0 / (Fs * oversampling_factor)))  # original signal
  25.  
  26. """plot the results"""
  27. plt.subplot(211)
  28. plt.plot(x, y_time)
  29. plt.xlim([0, n])
  30. plt.xlabel('sample')
  31. plt.subplot(212)
  32. plt.plot(x_freq, y_freq, label='original')
  33. plt.plot(x_freq_shifted, y_freq_shifted, label='shifted')
  34. plt.plot(x_freq_oversampled, y_freq_oversampled, label='oversampled')
  35. plt.legend()
  36. plt.xlim([0, Fs/2])
  37. plt.xlabel('frequency [Hz]')
  38. plt.show()
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