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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

help(scipy.signal.correlation_lags)

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

Parameters
----------
in1_len : int
    First input size.
in2_len : 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.

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.

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

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.

>>> import numpy as np
>>> from scipy import signal
>>> rng = np.random.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)]

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