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[9]:= 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[9]= (E^(-2 I Pi w) (1+E^(4 I Pi w)) Sin[Pi w])/(Pi w)
Regards,
Ssezi=
- References:
- FFT of the piecewise step function
- From: "Peng Yu" <pengyu.ut@gmail.com>
- FFT of the piecewise step function