Hilbert transform bug in 7.0.3?
- To: mathgroup at smc.vnet.net
- Subject: [mg100858] Hilbert transform bug in 7.0.3?
- From: Nacho <ncc1701zzz at gmail.com>
- Date: Tue, 16 Jun 2009 21:52:37 -0400 (EDT)
Hello.
I've trying the Hilbert Transform defined in Mathworld as:
HilbertTransform[f_, x_, y_, assum___?OptionQ] :=
Integrate[f/(x - y), {x, -Infinity, Infinity},
PrincipalValue -> True, assum]/Pi
I've trying to transform some functions but DiracDelta[x] seems to
fail:
In[5]:= HilbertTransform[DiracDelta[x],x,y]
Out[5]= 0
But it should be -1/(Pi y) according with Mathworld or 1/(Pi y)
according with Wikipedia, but not just 0. Older versions seems to
work, as you can see in Mathworld's notebook.
Is this a bug? Any other way to calculate Hilbert Transforms in
7.0.3?
Thanks.