jax.numpy.correlate¶
-
jax.numpy.
correlate
(a, v, mode='valid', *, precision=None)[source]¶ Cross-correlation of two 1-dimensional sequences.
LAX-backend implementation of
correlate()
. In addition to the original NumPy arguments listed below, also supportsprecision
for extra control over matrix-multiplication precision on supported devices.precision
may be set toNone
, which means default precision for the backend, alax.Precision
enum value (Precision.DEFAULT
,Precision.HIGH
orPrecision.HIGHEST
) or a tuple of twolax.Precision
enums indicating separate precision for each argument.Original docstring below.
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
v (a,) – 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 – Discrete cross-correlation of a and v.
- Return type
See also
convolve()
Discrete, linear convolution of two one-dimensional sequences.
multiarray.correlate()
Old, no conjugate, version of correlate.
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]
byc'_{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])