(Solved): Consider the periodic signal \( g(t) \), for which one period is shown in the figure below One Peri ...

Consider the periodic signal \( g(t) \), for which one period is shown in the figure below One Period of the periodic signal \( g(t) \) where \( \mathrm{A}=1 \) and \( T_{0}=0.1 \mathrm{sec} \). This signal can be expanded in a trigonometric Fourier series as: \[ g(t)=a_{0}+\sum_{n=1}^{\infty}\left(a_{n} \cos n \omega_{0} t+b_{n} \sin n \omega_{0} t\right) \] Now, consider the approximate signal: \[ g_{a}(t)=a_{0}+\sum_{n=1}^{K}\left(a_{n} \cos n \omega_{0} t+b_{n} \sin n \omega_{0} t\right) \] 1. Find \( a_{0}, a_{1}, a_{2}, a_{3}, b_{1}, b_{2} \), and \( b_{3} \) (you can use matlab or any other code to find numerical values of the coefficients) 2. Use matlab to plot \( g(t) \) and \( g_{a}(t) \) for \( K=3 \), on the same figure for one cycle of \( g(t) \). 3. The mean square error between \( g(t) \) and \( g_{a}(t) \) is defined as \[ M S E=\frac{1}{T_{0}}\left(\int_{0}^{T_{0}}\left(g(t)-g_{a}(t)\right)^{2} d t\right) \] Find the mean square error for \( \mathrm{K}=1,2 \), and 3 . Summarize your results in a table. 4. If \( g_{a}(t) \) (when \( K=3 \) ) is multiplied by the carrier \( c(t)=10 \cos 2 \pi(200) t \) followed by an ideal bandpass filter to generate the single sideband signal \( s(t) \), find \( s(t) \) and its spectrum.