Example of Computation of Fourier series of a CT SIGNAL
A practice problem on "Signals and Systems"
Defines the Fourier series of a periodic ct signal as
$ x(t) = \sum_{k=-\infty}^\infty a_k e^{jkw_0t} $
I set a example as
$ x(t)=6sin(2\pi t) + 4cos(4\pi t) $
$ =6*\frac{e^{2j\pi t} - e^{-2j\pi t}}{2j} + 4 *\frac{e^{4j\pi t} + e^{-4j\pi t}}{2} $
$ =3*\frac{e^{2j\pi t} - e^{-2j\pi t}}{j}+ 2 * (e^{4j\pi t}+e^{-4j\pi t}) $
$ a_1 = \frac{3}{j} $
$ a_2 = \frac{-3}{j} $
$ a_3 = 2 $
$ a_4=2 $
else
$ a_k = 0 $
$ w_0 = \pi $
