Re: Re: Fourier Transforms

*To*: mathgroup at smc.vnet.net*Subject*: [mg64815] Re: [mg64789] Re: [mg64762] Fourier Transforms*From*: Sseziwa Mukasa <mukasa at jeol.com>*Date*: Sat, 4 Mar 2006 02:35:30 -0500 (EST)*References*: <200603021148.GAA05247@smc.vnet.net> <200603030028.TAA29268@smc.vnet.net> <76e8f8180603030623y1d8ee0eftc74258212b9b2be@mail.gmail.com>*Sender*: owner-wri-mathgroup at wolfram.com

On Mar 3, 2006, at 9:23 AM, bsyehuda at gmail.com wrote: > I really cannot figure out how you got the 0 expression > both are unevaluated. I pasted the results from running this on Mathematica v5.0 on Max OS X 10.4.5. I did not do any analysis of the expressions. > 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? Only the first expression is odd, the second is even. > 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) You are correct that the Inverse Fourier Transform of the first expression should have some energy, perhaps this is a bug in version 5? > Some coarse approximation: > both function have a general form of a sign function The second expression actually looks like a Gaussian or Lorentzian. I would expect its spectrum to look like some kind of decaying sinusoid. Regards, Ssezi

**References**:**Fourier Transforms***From:*"Ben C" <benjamin.chamberlain@seh.ox.ac.uk>

**Re: Fourier Transforms***From:*Sseziwa Mukasa <mukasa@jeol.com>