Re: Re: FFT of the piecewise step function

*To*: mathgroup at smc.vnet.net*Subject*: [mg77888] Re: [mg77794] Re: FFT of the piecewise step function*From*: "Peng Yu" <pengyu.ut at gmail.com>*Date*: Tue, 19 Jun 2007 06:36:07 -0400 (EDT)*References*: <200706170959.FAA01403@smc.vnet.net>

On 6/17/07, Bill Rowe <readnewsciv at sbcglobal.net> wrote: > On 6/16/07 at 3:32 AM, pengyu.ut at gmail.com (Peng Yu) wrote: > > >mask[x_] := UnitStep[-(x - 1/2)(x + 1/2)(x - 3/2)(x + 3/2)] > >freq[=C3=B9_]:= FourierTransform[mask[t], t, =C3=B9] > > >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. > > You didn't say what version of Mathematica you are using. In > version 6, I get the following: > > In[6]:= m = UnitStep[-(x - 1/2) (x + 1/2) (x - 3/2) (x + 3/2)]; > =46ourierTransform[m, x, w] > > Out[7]= (Sqrt[2/Pi]*(Sin[(3*w)/2] - Sin[w/2]))/w > > In[8]:= $Version > > Out[8]= 6.0 for Mac OS X PowerPC (32-bit) (April 20, 2007) > > If you are not getting this, you might try using Simplify or FullSimplify I'm using this version. Even FullSimplify won't give me answer without Delta function. In[240]:= $Version Out[240]= 5.0 for Microsoft Windows (June 11, 2003)

**References**:**Re: FFT of the piecewise step function***From:*Bill Rowe <readnewsciv@sbcglobal.net>