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

  First define some input parameters for the signal:

      >>> A = 2.
      >>> w0 = 1.  # rad/sec
      >>> nin = 150
      >>> nout = 100000

  Randomly generate sample times:

      >>> x = rng.uniform(0, 10*np.pi, nin)

  Plot a sine wave for the selected times:

      >>> y = A * np.cos(w0*x)

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

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

  Calculate Lomb-Scargle periodogram:

      >>> import scipy.signal as signal
      >>> pgram = signal.lombscargle(x, y, w, normalize=True)

  Now make a plot of the input data:

      >>> fig, (ax_t, ax_w) = plt.subplots(2, 1, constrained_layout=True)
      >>> ax_t.plot(x, y, 'b+')
      >>> ax_t.set_xlabel('Time [s]')

  Then plot the normalized periodogram:

      >>> ax_w.plot(w, pgram)
      >>> ax_w.set_xlabel('Angular frequency [rad/s]')
      >>> ax_w.set_ylabel('Normalized amplitude')
      >>> plt.show()