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FFT of the piecewise step function


Hi,

mask[x_] := UnitStep[-(x - 1/2)(x + 1/2)(x - 3/2)(x + 3/2)]
freq[ù_] := FourierTransform[mask[t], t, ù]

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.

Thanks,
Peng


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