ASN2 - Something Interesting: Exponential

Fourier Series

Using cosine to represent the basis functions $x(t)=\sum _{n=0}^{\infty }a_{n}cos({\frac {2\pi nt}{T}})\!$

Using an exponential to represent basis functions $x(t)=\sum _{n=0}^{\infty }a_{n}e^{\frac {j2\pi nt}{T}}\!$

To obtain the coefffients $a_{n}$ the solutions are almost identical. The benefit of using the eponetial funtion is that mathematical it is simplier for solving than using the cosine function.