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# numpy.correlate

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

  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 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])