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Re: Why the FourierTransform gives two different answers?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg125138] Re: Why the FourierTransform gives two different answers?
*From*: Dana DeLouis <dana.del at gmail.com>
*Date*: Thu, 23 Feb 2012 05:49:31 -0500 (EST)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
> 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]
Hi. I don't have an answer, but an observation.
This seems strange, and I don't really see where the machine rounding
error is coming from.
If we take a basic formula of the Fourier equation, then the question is
why is the first part dropped to zero when done at machine precision.
FullSimplify[Integrate[(t - 5)^2*Exp[-(t - 5)^2], t]]
((-(1/2))*(-5 + t))/E^(-5 + t)^2 - (1/4)*Sqrt[Pi]*Erf[5 - t]
FullSimplify[Integrate[(t - 5.)^2*Exp[-(t - 5.)^2], t]]
0. - 0.44311346272637897*Erf[5. - 1.*t]
The difference is this part...
equ=-(1/2) E^-(-5+t)^2 (-5+t);
It plots nicely:
Plot[equ,{t,0,5}]
It has a nice value at 4:
N[equ] /.t->4
0.18394
But for some reason, simplifying it gives 0.
N[equ] //FullSimplify
0.
I don't have an explanation for this behavior (bug maybe??)
Even if we substitute w for t-5, it still doesn't reduce to zero at full
precision, and it does plot nicely.
FullSimplify[((-(1/2))*w)/E^w^2]
((-(1/2))*w)/E^w^2
= = = = = = = = = = = = = = =
HTH :>)
Dana DeLouis
Mac & Math 8
= = = = = = = = = = = = = = =
On Feb 21, 6:22 am, =D0=90=D0=BB=D0=B5=D0=BA=D1=81=D0=B5=D0=B9 <avde... at gmail.com> 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]
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