Solution

Past exam of the mathematics course of the University of Cambridge / 2017 / ii / Paper 3 / 20F / ii / Solution

Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 1 / 27J / b / Solution

For $f=\mathbf1_{[-a,a]}$ and the convention $\widehat f(\xi)=\int f(x)e^{-ix\xi}\,dx$,
$$
\widehat f(\xi)=\frac{2\sin(a\xi)}{\xi},
$$
with its continuous value $2a$ at zero.


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 Incoming links: Fourier transform of an interval indicator