Complicated periodic signals can be represented by a sum of cosine signals with frequencies that are integer multiples or "harmonics" of a fundamental frequency. This is the Fourier series.


Note about viewing mpegs.  Properties of a Fourier series can be demonstrated by viewing a cosine signal as the projection on the vertical axis of a rotating vector on the complex plane. Selecting this animation shows a cosine signal represented by a single phasor. 
A sum of cosine signals can be represented by projecting the vector sum of the individual phasors on the vertical axis. The vector sum is formed by placing the vectors in a "headtotail" fashion. Here is the sum of two cosines, the second wit h a nonzero phase angle. 

Here is a mathematical summary. 
Download Related Matlab mfiles 
Next Page 