View source for Fourier Series representation of continuous-time periodic signals (ECE301Summer2008asan) - Rhea

==Fourier Series representation of continuous-time periodic signals==
If x(t) = x(t + T) for all t (x(t) periodic with <math>\omega_0 = 2\pi/T</math>) 

 <math> 
\begin{align}
x(t) &= \Sigma_{k=-\infty}^{\infty} a_k e^{jk (2\pi/T) t} \\
\\ where \\
 a_k &= 1/T \int_{T}^{} x(t) e^{-jk (2\pi/T) t} dt
\end{align}
</math>