Module « scipy.signal »

Fonction correlation_lags - module scipy.signal

Signature de la fonction correlation_lags

def correlation_lags(in1_len, in2_len, mode='full') 

Description

correlation_lags.__doc__

    Calculates the lag / displacement indices array for 1D cross-correlation.

    Parameters
    ----------
    in1_size : int
        First input size.
    in2_size : int
        Second input size.
    mode : str {'full', 'valid', 'same'}, optional
        A string indicating the size of the output.
        See the documentation `correlate` for more information.

    See Also
    --------
    correlate : Compute the N-dimensional cross-correlation.

    Returns
    -------
    lags : array
        Returns an array containing cross-correlation lag/displacement indices.
        Indices can be indexed with the np.argmax of the correlation to return
        the lag/displacement.

    Notes
    -----
    Cross-correlation for continuous functions :math:`f` and :math:`g` is
    defined as:

    .. math ::

        \left ( f\star g \right )\left ( \tau \right )
        \triangleq \int_{t_0}^{t_0 +T}
        \overline{f\left ( t \right )}g\left ( t+\tau \right )dt

    Where :math:`\tau` is defined as the displacement, also known as the lag.

    Cross correlation for discrete functions :math:`f` and :math:`g` is
    defined as:

    .. math ::
        \left ( f\star g \right )\left [ n \right ]
        \triangleq \sum_{-\infty}^{\infty}
        \overline{f\left [ m \right ]}g\left [ m+n \right ]

    Where :math:`n` is the lag.

    Examples
    --------
    Cross-correlation of a signal with its time-delayed self.

    >>> from scipy import signal
    >>> from numpy.random import default_rng
    >>> rng = default_rng()
    >>> x = rng.standard_normal(1000)
    >>> y = np.concatenate([rng.standard_normal(100), x])
    >>> correlation = signal.correlate(x, y, mode="full")
    >>> lags = signal.correlation_lags(x.size, y.size, mode="full")
    >>> lag = lags[np.argmax(correlation)]