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Re: Fourier Transforms
*To*: mathgroup at smc.vnet.net
*Subject*: [mg64789] Re: [mg64762] Fourier Transforms
*From*: Sseziwa Mukasa <mukasa at jeol.com>
*Date*: Thu, 2 Mar 2006 19:28:19 -0500 (EST)
*References*: <200603021148.GAA05247@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
On Mar 2, 2006, at 6:48 AM, Ben C wrote:
> On the first of March I posted an appeal for help with some Fourier
> transforms. Since then a couple of people have suggested I post the
> actual transforms. I am trying to inverse Fourier transform the
> functions
>
> p / (sqrt(1+p^2 + sqrt(1+p^2 )) and 1/(sqrt(1+p^2 - sqrt(1+p^2 ))
>
> from p to x space.
>
> Any advice would again be extremely gratefully received,
You need to convert your expressions to proper Mathematica syntax,
sqrt(x) is Sqrt[x] in Mathematica. Since you're looking for a
symbolic solution use InverseFourierTransform like so:
In[3]:=
InverseFourierTransform[p/Sqrt[1+p^2+Sqrt[1+p^2]],p,x]
InverseFourierTransform[1/Sqrt[1+p^2-Sqrt[1+p^2]],p,x]
Out[3]=
0
Out[4]=
InverseFourierTransform[1/Sqrt[1+p^2-Sqrt[1+p^2]], p, x]
The second expression returns itself because the integral cannot be
performed. Perhaps your expression is only valid for p > 0? You
also need to specify the convention for the Fourier transform you are
using, see the Help Browser for more information.
Regards,
Ssezi
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