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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



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