Problem $4$: $[5+5$ points$]$

Given the exponential Fourier spectra of a periodic signal $x(t)$

$($a$)$ By inspection, find the exponential Fourier series representing $x(t).$

SOLUTION:

$($b$)$ Convert the exponential Fourier series representation of $x(t)$ into trigonometric Fourier series by using the Euler's identity: $\frac{e^{jx}+e^{-jx}}{2}=cosx.$