Mathematics Asked by user215736 on October 4, 2020

Find the Fourier transform of the unit rectangular distribution

f(t)=1 |t|<1

0 otherwise

Determine the convolution of f with itself and, without further integration, deduce its transform.

Deduce that

`mathint_{-inf}^{inf} frac{sin^2(w)}{w^2} = pimath`

I obtained the Fourier transform of f and the convulation with itself but cannot use it to evaluate te integral. The problem is from KF Riley- 13.7

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