Module « scipy.signal »

Fonction lombscargle - module scipy.signal

Signature de la fonction lombscargle

def lombscargle(x, y, freqs, precenter=False, normalize=False) 

Description

lombscargle.__doc__

    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.

    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

    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

    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()