ASN2 - Something Interesting: Exponential

Fourier Series

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

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

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.