Mathematica 9 is now available
Services & Resources / Wolfram Forums / MathGroup Archive
-----

MathGroup Archive 2009

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Hilbert transform bug in 7.0.3?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg100916] Re: Hilbert transform bug in 7.0.3?
  • From: did <didier.oslo at hotmail.com>
  • Date: Thu, 18 Jun 2009 04:52:45 -0400 (EDT)
  • References: <h19i5r$p4g$1@smc.vnet.net>

On Jun 17, 3:50 am, Nacho <ncc1701... at gmail.com> wrote:
> 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.

Try something like:

HilbertTransform[f_, x_, y_] :=
  Integrate[(f[y + x] - f[y - x])/x, {x, -Infinity,
Infinity},Assumptions -> y \[Element] Reals]/Pi/2;

HilbertTransform[DiracDelta, x, y]

and adapt it for the general case you need.


  • Prev by Date: Re: PDF import problem
  • Next by Date: Re: How to downsample a image matrix using left and right downsampling
  • Previous by thread: Re: Hilbert transform bug in 7.0.3?
  • Next by thread: Re: Hilbert transform bug in 7.0.3?