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Parseval Equation

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How to use parseval relation to get the solution pi for part b)? Please see the attach file.

A rectangular pulse is described by:
[see the attached file for the equation]

Show that the Fourier exponential transform is
[see the attached file for the equation]

This is the single-slit diffractional problem of physical optics. The slit is described by f(x). The diffraction pattern amplitude is given by the Fourier transform F(t).

Use the Parseval relation to evaluate
[see the attached file for the equation].

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The solution discusses how to use parseval relation to get the solution pi for part b.

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