       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

```

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