`scipy.signal._signaltools:correlation_lags`

source: /scipy/signal/_signaltools.py :317

Signature

def correlation_lags ( in1_len , in2_len , mode = full )

Summary

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.

Notes

Cross-correlation for continuous functions $f$ and $g$ is defined as:

(f ⋆ g) (τ) ≜ \int_{t_{0}}^{t_{0} + T} \overline{f (t)} g (t + τ) d t

Where $τ$ is defined as the displacement, also known as the lag.

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

(f ⋆ g) [n] ≜ - \infty \sum \infty \overline{f [m]} g [m + n]

Where $n$ is the lag.

Array API Standard Support

correlation_lags is not in-scope for support of Python Array API Standard compatible backends other than NumPy.

See dev-arrayapi for more information.

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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Aliases

scipy.signal.correlation_lags

Referenced by

This package

release:1.6.0-notes