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>