Example of Computation of Fourier series of a CT SIGNAL
A practice problem on "Signals and Systems"
$ \ x(t) = \cos(4t\pi /6) + \sin(3t \pi /6) $
$ x(t)=({ e^{j 4t\pi/6} + e^{-j4t\pi/6} \over 2}) + ({ e^{j3t\pi/6} - e^{-j3t\pi/6} \over 2j }) $
$ a_k=\frac{1}{T}\int_0^Tx(t)e^{-jk\omega_0t}dt $
$ T = 2\pi $
$ x(t)=({ e^{2\pi jt/3} + e^{-2\pi jt/3} \over 2}) + ({ e^{2\pi j3t/12} - e^{-2\pi j3t/12} \over 2j }) $
$ \ a_{1}= \frac{1}{2} $
$ a_{-1}= \frac{-1}{2} $
$ a_{3}= \frac{1}{2j} = \frac{j}{2} $
$ a_{-3}= \frac{-1}{2j} = \frac{-j}{2} $
