Signals and systems/GF Fourier

The Fourier series is used to analyze arbitrary periodic functions by showing them as a composite of sines and cosines. A function is considered periodic if $x(t)=x(t+T)$ for $T\ne 0$. The exponential form of the Fourier series is defined as $x(t)=\sum _{n=-\mathrm{\infty }}^{\mathrm{\infty }}{\alpha }_n{e}^{j2\pi nt/T}$

Notes

$e^{j\theta }=cos\theta +jsin\theta$