Problem $2$: $[4+6$ points$]$

Given the following compact trigonometric Fourier series representation of a periodic signal $x(t)$ of period $T_0=2,$ identify the coefficients $C_n$ and write down the MATLAB code lines to plot the $|C_n|$ versus the angular frequency $=n{}_0$ for $n=0,1,2,$dots,$10.$

$x(t)=\frac{1}{3}+\frac{4}{{}^2}{\displaystyle \underset{n=1}{\overset{}{}}}\frac{(-1{)}^n}{n^2}cosnt$

NOTE: Just jot down the code with proper values. The code must include proper labeling of the axes. We do not need the actual plot.

SOLUTION:

From the given representation of $x(t)$

$C_0=,C_0=\frac{1}{3}$

$C_n=,C_n=\frac{4}{{}^2}*\frac{(-m1{)}^n}{n^2}$

MATLAB Code: