`numpy:correlate`

source: /numpy/_core/numeric.py:725

Signature

def correlate(a, v, mode = valid)

Summary

Cross-correlation of two 1-dimensional sequences.

Extended Summary

This function computes the correlation as generally defined in signal processing texts ^[1]:

c_{k} = n \sum a_{n + k} \cdot \overline{v}_{n}

with a and v sequences being zero-padded where necessary and $\overline{v}$ denoting complex conjugation.

Parameters

a, v : array_like: Input sequences.
mode : {'valid', 'same', 'full'}, optional: Refer to the convolve docstring. Note that the default is 'valid', unlike convolve, which uses 'full'.

Returns

out : ndarray: Discrete cross-correlation of a and v.

Notes

The definition of correlation above is not unique and sometimes correlation may be defined differently. Another common definition is ^[1]:

c_{k}^{'} = n \sum a_{n} \cdot \overline{v_{n + k}}

which is related to $c_{k}$ by $c_{k}^{'} = c_{- k}$ .

numpy.correlate may perform slowly in large arrays (i.e. n = 1e5) because it does not use the FFT to compute the convolution; in that case, scipy.signal.correlate might be preferable.

Examples

import numpy as np
np.correlate([1, 2, 3], [0, 1, 0.5])

✓

array([3.5])

np.correlate([1, 2, 3], [0, 1, 0.5], "same")
np.correlate([1, 2, 3], [0, 1, 0.5], "full")

✗

array([0.5, 2. , 3.5, 3. , 0. ])

Using complex sequences:

np.correlate([1+1j, 2, 3-1j], [0, 1, 0.5j], 'full')

✗

array([0.5-0.5j, 1. +0.j , 1.5-1.5j, 3. -1.j , 0. +0.j ])

Note that you get the time reversed, complex conjugated result (:math:`\overline{c_{-k}}`) when the two input sequences a and v change places:

np.correlate([0, 1, 0.5j], [1+1j, 2, 3-1j], 'full')

✗

array([0. +0.j , 3. +1.j , 1.5+1.5j, 1. +0.j , 0.5+0.5j])

Aliases

numpy.correlate