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DOC: document sign convention in fftpack.hilbert. Closes #1506.

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1 parent 74dccec commit 9001996c765e148af5139089a1b3a2492e1f380b @rgommers rgommers committed Sep 11, 2011
Showing with 23 additions and 4 deletions.
  1. +23 −4 scipy/fftpack/pseudo_diffs.py
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27 scipy/fftpack/pseudo_diffs.py
@@ -168,10 +168,29 @@ def hilbert(x,
y_j = sqrt(-1)*sign(j) * x_j
y_0 = 0
- Notes:
- If sum(x,axis=0)==0 then
- hilbert(ihilbert(x)) == x
- For even len(x), the Nyquist mode of x is taken zero.
+ Parameters
+ ----------
+ x : array_like
+ The input array, should be periodic.
+ _cache : dict, optional
+ Dictionary that contains the kernel used to do a convolution with.
+
+ Returns
+ -------
+ y : ndarray
+ The transformed input.
+
+ Notes
+ -----
+ If ``sum(x, axis=0) == 0`` then ``hilbert(ihilbert(x)) == x``.
+
+ For even len(x), the Nyquist mode of x is taken zero.
+
+ The sign of the returned transform does not have a factor -1 that is more
+ often than not found in the definition of the Hilbert transform. Note also
+ that ``scipy.signal.hilbert`` does have an extra -1 factor compared to this
+ function.
+
"""
tmp = asarray(x)
if iscomplexobj(tmp):

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