(a) Determine the Fourier transform F(k) of the rectangular function f(x) = 1 for -a/2 ≤ x ≤a/2 f(x) = 0 elsewhere (b) What is the smallest k value for which F(k)=0? This defines the central peak width W. How does W changes if a is halved? (c) Plot F(k) versus k (use either Python, Matlab, Mathematica, Wolfram Alpha, or sketch by hand). Find the smallest value kmin of k such as F(kmin)= F(k=0)/10. This defines how far you have to go in k to have a good approximation of the rectangular function. Qualitatively, how does kmin evolves with a?