diff options
Diffstat (limited to 'numpy/core')
| -rw-r--r-- | numpy/core/numeric.py | 28 |
1 files changed, 27 insertions, 1 deletions
diff --git a/numpy/core/numeric.py b/numpy/core/numeric.py index 53254ec6a..f43f93d64 100644 --- a/numpy/core/numeric.py +++ b/numpy/core/numeric.py @@ -823,7 +823,7 @@ def correlate(a, v, mode='valid', old_behavior=False): This function computes the correlation as generally defined in signal processing texts:: - z[k] = sum_n a[n] * conj(v[n+k]) + 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. @@ -841,10 +841,24 @@ 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 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]) @@ -854,6 +868,18 @@ 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., + ``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 |