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MathGroup Archive 2006

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Re: Re: Fourier Transforms


I really cannot figure out how you got the 0 expression both are unevaluated.
To Ben C.
I see that these are odd functions, pointing the the functions in the x
domain are not real. are you aware of that fact?
In addition, if this is the spectrum of some function, it should include
infinite energy, pointing on its behaviour (the spectrum is not
band-limited) (dirac delta, or some infinite value near the origin)
Some coarse approximation:
both function have a general form of a sign function
yehuda

yehuda

On 3/3/06, Sseziwa Mukasa <mukasa at jeol.com> wrote:
>
>
> 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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