Fourier Example: Difference between revisions

Revision as of 00:28, 19 January 2010

Find the Fourier Series of the function:

f(x)={\begin{cases}0,&-\pi <x<0\\\pi ,&0<x<\pi \\\end{cases}}

b_{n}={\frac {1}{2}}{\pi }\int _{0}^{\pi }\pi \sin(nx)\,dx,={\frac {1}{n}}(1-cos(x\pi ))={\frac {1}{n}}(1-(-1)^{n})

@@ Line 1: / Line 1: @@
 Find the Fourier Series of the function:
+:<math>f(x) = \begin{cases}0,& -\pi<x<0\\
-<br />
+\pi,& 0<x<\pi\\
+\end{cases}</math>
+:<math>b_n = \frac{1}{2}{\pi}\int_{0}^\pi  \pi\sin(nx)\, dx, = \frac{1}{n}(1-cos(x\pi))=\frac{1}{n}(1-(-1)^n)</math>
-<center><math>\f(x)=begin{cases}
-,-pi<x<0
-\end{cases} \ \ \ \ n=0,1,2,3\dots</math></center>
-<br />
-:<math>\rho_X(x) = \begin{cases}\frac{1}{2},& \x=0,\\
-\frac{1}{2},& \x=1,\\
-,& \text{otherwise} .\end{cases}</math>
- <!--  -->