numpy.correlate¶
- numpy.correlate(a, v, mode='valid')[source]¶
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
old_behavior : bool
old_behavior was removed in NumPy 1.10. If you need the old behavior, use multiarray.correlate.
Returns: out : ndarray
Discrete cross-correlation of a and v.
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] 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])