scipy.signal.lombscargle#

scipy.signal.lombscargle(x, y, freqs)[source]#

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:

xarray_like: Sample times.
yarray_like: Measurement values.
freqsarray_like: Angular frequencies for output periodogram.
precenterbool, optional: Pre-center measurement values by subtracting the mean.
normalizebool, optional: Compute normalized periodogram.

Returns:

pgramarray_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()

../../_images/scipy-signal-lombscargle-1.png