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Fonction csd - module scipy.signal

Signature de la fonction csd

def csd(x, y, fs=1.0, window='hann', nperseg=None, noverlap=None, nfft=None, detrend='constant', return_onesided=True, scaling='density', axis=-1, average='mean') 

Description

csd.__doc__

    Estimate the cross power spectral density, Pxy, using Welch's method.

    Parameters
    ----------
    x : array_like
        Time series of measurement values
    y : array_like
        Time series of measurement values
    fs : float, optional
        Sampling frequency of the `x` and `y` time series. Defaults
        to 1.0.
    window : str or tuple or array_like, optional
        Desired window to use. If `window` is a string or tuple, it is
        passed to `get_window` to generate the window values, which are
        DFT-even by default. See `get_window` for a list of windows and
        required parameters. If `window` is array_like it will be used
        directly as the window and its length must be nperseg. Defaults
        to a Hann window.
    nperseg : int, optional
        Length of each segment. Defaults to None, but if window is str or
        tuple, is set to 256, and if window is array_like, is set to the
        length of the window.
    noverlap: int, optional
        Number of points to overlap between segments. If `None`,
        ``noverlap = nperseg // 2``. Defaults to `None`.
    nfft : int, optional
        Length of the FFT used, if a zero padded FFT is desired. If
        `None`, the FFT length is `nperseg`. Defaults to `None`.
    detrend : str or function or `False`, optional
        Specifies how to detrend each segment. If `detrend` is a
        string, it is passed as the `type` argument to the `detrend`
        function. If it is a function, it takes a segment and returns a
        detrended segment. If `detrend` is `False`, no detrending is
        done. Defaults to 'constant'.
    return_onesided : bool, optional
        If `True`, return a one-sided spectrum for real data. If
        `False` return a two-sided spectrum. Defaults to `True`, but for
        complex data, a two-sided spectrum is always returned.
    scaling : { 'density', 'spectrum' }, optional
        Selects between computing the cross spectral density ('density')
        where `Pxy` has units of V**2/Hz and computing the cross spectrum
        ('spectrum') where `Pxy` has units of V**2, if `x` and `y` are
        measured in V and `fs` is measured in Hz. Defaults to 'density'
    axis : int, optional
        Axis along which the CSD is computed for both inputs; the
        default is over the last axis (i.e. ``axis=-1``).
    average : { 'mean', 'median' }, optional
        Method to use when averaging periodograms. If the spectrum is
        complex, the average is computed separately for the real and
        imaginary parts. Defaults to 'mean'.

        .. versionadded:: 1.2.0

    Returns
    -------
    f : ndarray
        Array of sample frequencies.
    Pxy : ndarray
        Cross spectral density or cross power spectrum of x,y.

    See Also
    --------
    periodogram: Simple, optionally modified periodogram
    lombscargle: Lomb-Scargle periodogram for unevenly sampled data
    welch: Power spectral density by Welch's method. [Equivalent to
           csd(x,x)]
    coherence: Magnitude squared coherence by Welch's method.

    Notes
    -----
    By convention, Pxy is computed with the conjugate FFT of X
    multiplied by the FFT of Y.

    If the input series differ in length, the shorter series will be
    zero-padded to match.

    An appropriate amount of overlap will depend on the choice of window
    and on your requirements. For the default Hann window an overlap of
    50% is a reasonable trade off between accurately estimating the
    signal power, while not over counting any of the data. Narrower
    windows may require a larger overlap.

    .. versionadded:: 0.16.0

    References
    ----------
    .. [1] P. Welch, "The use of the fast Fourier transform for the
           estimation of power spectra: A method based on time averaging
           over short, modified periodograms", IEEE Trans. Audio
           Electroacoust. vol. 15, pp. 70-73, 1967.
    .. [2] Rabiner, Lawrence R., and B. Gold. "Theory and Application of
           Digital Signal Processing" Prentice-Hall, pp. 414-419, 1975

    Examples
    --------
    >>> from scipy import signal
    >>> import matplotlib.pyplot as plt
    >>> rng = np.random.default_rng()

    Generate two test signals with some common features.

    >>> fs = 10e3
    >>> N = 1e5
    >>> amp = 20
    >>> freq = 1234.0
    >>> noise_power = 0.001 * fs / 2
    >>> time = np.arange(N) / fs
    >>> b, a = signal.butter(2, 0.25, 'low')
    >>> x = rng.normal(scale=np.sqrt(noise_power), size=time.shape)
    >>> y = signal.lfilter(b, a, x)
    >>> x += amp*np.sin(2*np.pi*freq*time)
    >>> y += rng.normal(scale=0.1*np.sqrt(noise_power), size=time.shape)

    Compute and plot the magnitude of the cross spectral density.

    >>> f, Pxy = signal.csd(x, y, fs, nperseg=1024)
    >>> plt.semilogy(f, np.abs(Pxy))
    >>> plt.xlabel('frequency [Hz]')
    >>> plt.ylabel('CSD [V**2/Hz]')
    >>> plt.show()