Re: problem
- To: mathgroup at smc.vnet.net
- Subject: [mg23699] Re: [mg23664] problem
- From: BobHanlon at aol.com
- Date: Mon, 29 May 2000 12:24:28 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
In a message dated 5/28/2000 11:23:21 PM, hochimin at nexlinx.net.pk writes:
>I can't figure out the inverse fourier transform of the following function:
>H(w)= 1 |x|<1,
> 0 |x|>1
>
H[w_] := UnitStep[w + 1] - UnitStep[w - 1]
Plot[H[w], {w, -2, 2}];
f[t_] := Evaluate[InverseFourierTransform[H[w], w, t] // FullSimplify]
f[t]
(Sqrt[2/Pi]*Sin[t])/t
Plot[f[t], {t, -2Pi, 6Pi}, PlotRange -> All];
FourierTransform[f[t], t, w]
1/2*(Sign[1 - w] + Sign[w + 1])
This is an alternate representation for H[w]
Plot[%, {w, -2, 2}];
(InverseFourierTransform[%%, w, t] // Expand // FullSimplify) == f[t]
True
Bob
BobHanlon at aol.com