scipy.signal.correlation_lags

scipy.signal.correlation_lags(in1_len, in2_len, mode='full')

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

Parameters:

in1_lenint

First input size.

in2_lenint

Second input size.

modestr {‘full’, ‘valid’, ‘same’}, optional

A string indicating the size of the output. See the documentation correlate for more information.

Returns:

lagsarray

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 \(f\) and \(g\) is defined as:

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

Where \(\tau\) is defined as the displacement, also known as the lag.

Cross correlation for discrete functions \(f\) and \(g\) is defined as:

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

Where \(n\) 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)]