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# scipy.signal.lombscargle

`scipy.signal.``lombscargle`(x, y, freqs)

  Computes the Lomb-Scargle periodogram.

  The Lomb-Scargle periodogram was developed by Lomb [R191] and further extended by Scargle [R192] to find, and test the significance of weak periodic signals with uneven temporal sampling.

  The computed periodogram is unnormalized, it takes the value `(A**2) * N/4` for a harmonic signal with amplitude A for sufficiently large N.

  Parameters: | x : array_like Sample times. y : array_like Measurement values. freqs : array_like Angular frequencies for output periodogram.
  Returns: | pgram : array_like Lomb-Scargle periodogram.
  Raises: | ValueError If the input arrays x and y do not have the same shape.

  Notes

  This subroutine calculates the periodogram using a slightly modified algorithm due to Townsend [R193] which allows the periodogram to be calculated using only a single pass through the input arrays for each frequency.

  The algorithm running time scales roughly as O(x * freqs) or O(N^2) for a large number of samples and frequencies.

  References

  [R191] | (1, 2) N.R. Lomb “Least-squares frequency analysis of unequally spaced data”, Astrophysics and Space Science, vol 39, pp. 447-462, 1976

  [R192] | (1, 2) J.D. Scargle “Studies in astronomical time series analysis. II - Statistical aspects of spectral analysis of unevenly spaced data”, The Astrophysical Journal, vol 263, pp. 835-853, 1982

  [R193] | (1, 2) R.H.D. Townsend, “Fast calculation of the Lomb-Scargle periodogram using graphics processing units.”, The Astrophysical Journal Supplement Series, vol 191, pp. 247-253, 2010

  Examples

      >>> import scipy.signal
      >>> import matplotlib.pyplot as plt

  First define some input parameters for the signal:

      >>> A = 2.
      >>> w = 1.
      >>> phi = 0.5 * np.pi
      >>> nin = 1000
      >>> nout = 100000
      >>> frac_points = 0.9 # Fraction of points to select

  Randomly select a fraction of an array with timesteps:

      >>> r = np.random.rand(nin)
      >>> x = np.linspace(0.01, 10*np.pi, nin)
      >>> x = x[r >= frac_points]
      >>> normval = x.shape[0] # For normalization of the periodogram

  Plot a sine wave for the selected times:

      >>> y = A * np.sin(w*x+phi)

  Define the array of frequencies for which to compute the periodogram:

      >>> f = np.linspace(0.01, 10, nout)

  Calculate Lomb-Scargle periodogram:

      >>> import scipy.signal as signal
      >>> pgram = signal.lombscargle(x, y, f)

  Now make a plot of the input data:

      >>> plt.subplot(2, 1, 1)
      <matplotlib.axes.AxesSubplot object at 0x102154f50>
      >>> plt.plot(x, y, 'b+')
      [<matplotlib.lines.Line2D object at 0x102154a10>]

  Then plot the normalized periodogram:

      >>> plt.subplot(2, 1, 2)
      <matplotlib.axes.AxesSubplot object at 0x104b0a990>
      >>> plt.plot(f, np.sqrt(4*(pgram/normval)))
      [<matplotlib.lines.Line2D object at 0x104b2f910>]
      >>> plt.show()

  (Source code)