diff options
Diffstat (limited to 'numpy/core/numeric.py')
| -rw-r--r-- | numpy/core/numeric.py | 22 |
1 files changed, 11 insertions, 11 deletions
diff --git a/numpy/core/numeric.py b/numpy/core/numeric.py index b89bbe457..bb3cbf054 100644 --- a/numpy/core/numeric.py +++ b/numpy/core/numeric.py @@ -675,16 +675,16 @@ def _correlate_dispatcher(a, v, mode=None): @array_function_dispatch(_correlate_dispatcher) def correlate(a, v, mode='valid'): - """ + r""" Cross-correlation of two 1-dimensional sequences. This function computes the correlation as generally defined in signal - processing texts:: + processing texts: - c_{av}[k] = sum_n a[n+k] * conj(v[n]) + .. math:: c_k = \sum_n a_{n+k} \cdot \overline{v_n} - with a and v sequences being zero-padded where necessary and conj being - the conjugate. + with a and v sequences being zero-padded where necessary and + :math:`\overline x` denoting complex conjugation. Parameters ---------- @@ -711,11 +711,11 @@ def correlate(a, v, mode='valid'): Notes ----- The definition of correlation above is not unique and sometimes correlation - may be defined differently. Another common definition is:: + may be defined differently. Another common definition is: - c'_{av}[k] = sum_n a[n] conj(v[n+k]) + .. math:: c'_k = \sum_n a_{n} \cdot \overline{v_{n+k}} - which is related to ``c_{av}[k]`` by ``c'_{av}[k] = c_{av}[-k]``. + which is related to :math:`c_k` by :math:`c'_k = c_{-k}`. `numpy.correlate` may perform slowly in large arrays (i.e. n = 1e5) because it does not use the FFT to compute the convolution; in that case, `scipy.signal.correlate` might @@ -737,8 +737,8 @@ def correlate(a, v, mode='valid'): 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]``: + (:math:`\overline{c_{-k}}`) when the two input sequences a and v change + places: >>> 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]) @@ -804,7 +804,7 @@ def convolve(a, v, mode='full'): ----- The discrete convolution operation is defined as - .. math:: (a * v)[n] = \\sum_{m = -\\infty}^{\\infty} a[m] v[n - m] + .. math:: (a * v)_n = \\sum_{m = -\\infty}^{\\infty} a_m v_{n - m} It can be shown that a convolution :math:`x(t) * y(t)` in time/space is equivalent to the multiplication :math:`X(f) Y(f)` in the Fourier |