The signal used
In this example, I am using the signal $ x(t)=cos(2t) + 2sin(2t)\! $.
Coefficient Breakdown
To get the coefficients of a simple signal like this, we have to expand it.
$ x(t)=\frac{e^{2jt}}{2}+ \frac{e^{-2jt}} {2}+ 2\frac{e^{2jt}} {2j}+ 2\frac{e^{-2jt}} {2j}! $
$ \omega_0\! $ is $ 2 \! $ in this example.
$ a_{1,-1}=\frac{1}{2}\! $
$ a_{2,-2}=\frac{1}{j}\! $
