Re: Why the FourierTransform gives two different answers?
- To: mathgroup at smc.vnet.net
- Subject: [mg125135] Re: Why the FourierTransform gives two different answers?
- From: "Nasser M. Abbasi" <nma at 12000.org>
- Date: Thu, 23 Feb 2012 05:48:28 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <jhvupg$893$1@smc.vnet.net>
- Reply-to: nma at 12000.org
On 2/22/2012 3:25 AM, Nasser M. Abbasi wrote: > On 2/21/2012 5:22 AM, Ð?лекÑ?ей wrote: >> Why the FourierTransform gives two different answers? >> >> In[1] FourierTransform[ (t - 5.0)^2*Exp[-(t - 5.0)^2 ], t, w] >> >> In[2] FourierTransform[ (t - 5)^2* Exp[-(t - 5)^2 ], t, w] >> .... > > ------------ symbolic ----------- > ClearAll[t, w, k] > f = (t - 5)^2*Exp[-(t - 5)^2]; > res = Integrate[f*Exp[-I w t], {t, -k, k}]; > res = Limit[res, k -> Infinity]; > Plot[{Re[res], Im[res]}, {w, -5, 5}] > ----------------------------- > ... btw, to get the same result with Mathematica FourierTransform need to use FourierParameters -> {1, -1}, like this: --------------------------- ClearAll[t, w, k] f = (t - 5)^2*Exp[-(t - 5)^2]; res = FourierTransform[f, t, w, FourierParameters -> {1, -1}]; Plot[{Re[res], Im[res]}, {w, -5, 5}] -------------------------- --Nasser