$(10$p$)$ Consider the following signal sxpol$(t)=\frac{4}{}{\displaystyle \underset{k=0}{\overset{4}{}}}\frac{1}{2n+1}sin[(2n+1)\frac{2}{T}t],$ where $T=0\mathrm{.}01s.$

a$.(4$p$)$ Plot the signal, for a time window $-\frac{T}{2},\frac{T}{2}.$ Consider $1000$ points when generating the Python plot.

b$.(1$p$)$ Consider representing sxpol as a sum of $cos()$ signals; $1)[$:$\frac{2}{T}t-\frac{}{2}\},$ where $A_k$ and ${}_k$ are the amplitude and the phase of the sinusoid on frequency $f_k,$ respectively. Recall that the equation for a signals is where are

c$.(1$p$)$ What are the set of frequencies $f_k$ in $sx(t)?$

d$.(2p+2p)$ Create a python plot the includes both the amplitude spectrum $A_k(f_k)$ and the phase spectrum ${}_k(f_k)$ for the signal $sx(t).$ The frequency axes must be identical for both plots Hint$1$: the amplitude spectrum has $A_k$ on the $y-$axis and $f_k$ on the x$-$axis Hint $2$: use plt$.$stem$()$ for the plots at this point

$(10$p$)$ Consider the $32$ matrix $A=\left[\begin{array}{cc}7& 8\\ 4& 5\\ 1& 2\end{array}\right]=\left[\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\\ a_{31}& a_{32}\end{array}\right].$ Write the Python code for:

a$.(2$p$)$ Initializing matrix A$.$ Use for the Python variable the name "matrixA".

b$.(1$p$)$ Finding the shape for matrixA

c$.(2$p$)$ Getting $a_{22}$

d$.(2$p$)$ Getting the second row of $A$

e$.(2$p$)$ Getting the first column of A

f$.(1$p$)$ Can we compute the inverse $A^{-1}?$ Why?