# Exponential Fourier-series expansion

• April 14th 2009, 04:33 PM
tiki_master
Exponential Fourier-series expansion
I need help in determining the exponential fourier series expansion for the half-wave rectified signal x(t)=cos(t). I am trying to find Xn, and have determined for the case where n=0, Xn=1/pi...but I'm having trouble finding the general case for just Xn. Any help would be appreciated.
• May 23rd 2009, 06:48 PM
Media_Man
Fourier Series
$f(x)=\frac{1}{2}a_0+\sum_{n=1}^\infty a_n\cos(nx)+\sum_{n=1}^\infty b_n\sin(nx)$

$a_0=\frac{1}{\pi}\int_{-\pi}^\pi f(x)dx$

$a_n=\frac{1}{\pi}\int_{-\pi}^\pi f(x)\cos(nx)dx$

$b_n=\frac{1}{\pi}\int_{-\pi}^\pi f(x)\sin(nx)dx$

Look very, very carefully at the function you are trying to expand here. $x(t)=cos(t)$, therefore $a_0=0$, $a_1=1$, $a_n=0$ for all $n>1$, and $b_n=0$ for all $n$.