# scipy.signal.lombscargle

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

  Computes the Lomb-Scargle periodogram.

  The Lomb-Scargle periodogram was developed by Lomb [1] and further extended by Scargle [2] to find, and test the significance of weak periodic signals with uneven temporal sampling.

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

  When normalize is True the computed periodogram is normalized by the residuals of the data around a constant reference model (at zero).

  Input arrays should be 1-D and will be cast to float64.

  Parameters
    x array_like

      Sample times.

    y array_like

      Measurement values.

    freqs array_like

      Angular frequencies for output periodogram.

    precenter bool, optional

      Pre-center measurement values by subtracting the mean.

    normalize bool, optional

      Compute normalized periodogram.

  Returns
    pgram array_like

      Lomb-Scargle periodogram.

  Raises
    ValueError

      If the input arrays x and y do not have the same shape.

  See also

  `istft`

    Inverse Short Time Fourier Transform

  `check_COLA`

    Check whether the Constant OverLap Add (COLA) constraint is met

  `welch`

    Power spectral density by Welch’s method

  `spectrogram`

    Spectrogram by Welch’s method

  `csd`

    Cross spectral density by Welch’s method

  Notes

  This subroutine calculates the periodogram using a slightly modified algorithm due to Townsend [3] 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

  1

    N.R. Lomb “Least-squares frequency analysis of unequally spaced data”, Astrophysics and Space Science, vol 39, pp. 447-462, 1976

  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

  3

    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 matplotlib.pyplot as plt
      >>> rng = np.random.default_rng()

  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 = rng.standard_normal(nin)
      >>> x = np.linspace(0.01, 10*np.pi, nin)
      >>> x = x[r >= frac_points]

  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, normalize=True)

  Now make a plot of the input data:

      >>> plt.subplot(2, 1, 1)
      >>> plt.plot(x, y, 'b+')

  Then plot the normalized periodogram:

      >>> plt.subplot(2, 1, 2)
      >>> plt.plot(f, pgram)
      >>> plt.show()

scipy.signal.spectrogram scipy.signal.vectorstrength