Create a Matlab script to reproduce Figure $3\mathrm{.}1.$ Ex$-$ periment with other values of N$.$ Describe what you see. Near the jump discontinuity you will see an overshoot that remains large as N increases. This is the Gibbs phenomenon$1.$ Repeat the exercise for the square wave function that arises as the periodic extension of Figure $3\mathrm{.}1.$ Graphs of the sawtooth function $f$ and its partial

Fourier sums $S_{N}f,$ for $N=2,5,$ and $20,$ extended periodically

from $[-,)$ to $R.$ Compare with Figure $3\mathrm{.}2.$

following step function $g()$ :

$g()=\{\begin{array}{ccc}1,& ifin[0,& )\\ -1,& ifin[-,& 0).\end{array}$

The project in Section $3\mathrm{.}4$ outlines a more detailed investigation of

the Gibbs phenomenon. $$I need code for this quesiton$$