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Re: FFT of the piecewise step function


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
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