numpy.correlate

numpy.correlate(a, v, mode='valid', old_behavior=False)

Cross-correlation of two 1-dimensional sequences.

This function computes the correlation as generally defined in signal processing texts:

c_{av}[k] = sum_n a[n+k] * conj(v[n])

with a and v sequences being zero-padded where necessary and conj being the conjugate.

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.

old_behavior : bool

If True, uses the old behavior from Numeric, (correlate(a,v) == correlate(v,a), and the conjugate is not taken for complex arrays). If False, uses the conventional signal processing definition.

Returns:

out : ndarray

Discrete cross-correlation of a and v.

See also

convolve

Discrete, linear convolution of two one-dimensional sequences.

Notes

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

c'_{av}[k] = sum_n a[n] conj(v[n+k])

which is related to c_{av}[k] by c'_{av}[k] = c_{av}[-k].

Examples

>>> np.correlate([1, 2, 3], [0, 1, 0.5])
array([ 3.5])
>>> np.correlate([1, 2, 3], [0, 1, 0.5], "same")
array([ 2. ,  3.5,  3. ])
>>> 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+0.j ,  1.5-1.5j,  3.0-1.j ,  0.0+0.j ])

Note that you get the time reversed, complex conjugated result when the two input sequences change places, i.e., c_{va}[k] = c^{*}_{av}[-k]:

>>> np.correlate([0, 1, 0.5j], [1+1j, 2, 3-1j], 'full')
array([ 0.0+0.j ,  3.0+1.j ,  1.5+1.5j,  1.0+0.j ,  0.5+0.5j])