diff options
Diffstat (limited to 'numpy/core/numeric.py')
| -rw-r--r-- | numpy/core/numeric.py | 41 |
1 files changed, 34 insertions, 7 deletions
diff --git a/numpy/core/numeric.py b/numpy/core/numeric.py index 1aa59ce58..a5f6140f1 100644 --- a/numpy/core/numeric.py +++ b/numpy/core/numeric.py @@ -820,13 +820,8 @@ def 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:: - - z[k] = sum_n a[n] * conj(v[n+k]) - - with a and v sequences being zero-padded where necessary and conj being - the conjugate. + This function computes the cross-correlation of two sequences a and v + as generally defined in signal processing text. Parameters ---------- @@ -841,10 +836,30 @@ def correlate(a, v, mode='valid', old_behavior=False): 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 discrete cross-correlation of two sequences a and v is defined as + + .. math:: c_{av}[k] = \\sum_{n = -\\infty}^{\\infty} a[n+k] v^{*}[n] + + where :math:`v^{*}[n]` is the complex conjugate of :math:`v[n]`. + + Note that sometimes correlation may be defined differently. + Another common definition is + + .. math:: c'_{av}[k] = \\sum_{n = -\\infty}^{\\infty} a[n] v^{*}[n+k] + + which is related to :math:`c_{av}[k]` by :math:`c'_{av}[k] = c_{av}[-k]`. + Examples -------- >>> np.correlate([1, 2, 3], [0, 1, 0.5]) @@ -854,6 +869,18 @@ def correlate(a, v, mode='valid', old_behavior=False): >>> 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., + :math:`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]) + """ mode = _mode_from_name(mode) # the old behavior should be made available under a different name, see thread |