Re: Fourier transform of exponential function
- To: mathgroup at smc.vnet.net
- Subject: [mg108639] Re: Fourier transform of exponential function
- From: "Kevin J. McCann" <Kevin.McCann at umbc.edu>
- Date: Thu, 25 Mar 2010 06:32:23 -0500 (EST)
- References: <hofg7f$f89$1@smc.vnet.net>
I suggest that you look at the integral you are trying to do. It is not clear from your post whether you mean to have t run from zero to infinity or from minus infinity to infinity. In the latter case, the integral does not converge, and this is what corresponds to your example. I suspect that you mean to take the FT of exp(-t) for t>0, i.e. the function is zero for negative t. If that is so, you could try FourierTransform[UnitStep[t] Exp[-t], t, w] with result: I/(Sqrt[2 \[Pi]] (I + w)) I am not sure why V5 and V7 give different results. Perhaps it is a feature ;). Kevin ALittleDog wrote: > I am trying to do a Fourier transform of a simple exponential > function, by using the following code: > FourierTransform[Exp[-t], t, =F9] > By Mahtematica 5.0, I obtain > \sqrt(2 Pi) DiracDelta[ I + =F9 ] > By Mathematica 7.0, I obtain a repetition of the original input as > FourierTransform[Exp[-t], t, =F9]. > > I search to look for a classical solution, but most of them are > talking about FourierTransform[Exp[-Abs[t]], t, =F9]. Indeed, what is > the classical solution of this problem? Why 5.0 version and 7.0 > version try to figure it out in a different manner? Thanks! > > >