       Re: FFT of the piecewise step function

• To: mathgroup at smc.vnet.net
• Subject: [mg77792] Re: [mg77769] FFT of the piecewise step function
• From: Sseziwa Mukasa <mukasa at jeol.com>
• Date: Sun, 17 Jun 2007 05:58:44 -0400 (EDT)
• References: <200706160732.DAA25970@smc.vnet.net>

```On Jun 16, 2007, at 3:32 AM, Peng Yu wrote:

> Hi,
>
> mask[x_] := UnitStep[-(x - 1/2)(x + 1/2)(x - 3/2)(x + 3/2)]
> freq[=F9_] := FourierTransform[mask[t], t, =F9]
>
> The solution of freq includes several DiracDelta functions, which
> should cancel out.
>
> I'm wondering if there is anyway to make mathematica cancel them out.

In this particular case it's easier to just use Integrate explicitly:

In:= Simplify[Integrate[Exp[-2 Pi I w t],{t,1/2,3/2}]+Integrate[Exp=

[-2 Pi I w t],{t,-3/2,-1/2}]]
Out= (E^(-2 I Pi w) (1+E^(4 I Pi w)) Sin[Pi w])/(Pi w)

Regards,

Ssezi=

```

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