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Find the Fourier transform of f (x) = {(1, |x| < a), (0, |x| > a)

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The Fourier transform of f (x) is

The graphs of f (x) and T (u) for u = 3 are shown in Fig. 1.9a, b, respectively 

Note that the above transform finds an application in the FraunHofer diffraction. 

˜f (ω) = A sin α/α 

This is the basic equation which describes the Fraunhofer’s diffraction pattern due to a single slit.

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