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, & - π < x < 0 \\ π, & 0 < x < π \end{cases}

b_{n} = \frac{1}{2} π \int_{0}^{π} π \sin (n x) d x, = \frac{1}{n} (1 - c o s (x π)) = \frac{1}{n} (1 - (- 1)^{n})

@@ Line 1: / Line 1: @@
 Find the Fourier Series of the function:
-<br />
+:<math>f(x) = \begin{cases}0,& -\pi<x<0\\
+\pi,& 0<x<\pi\\
+\end{cases}</math>
-<center><math>\f(x)=begin{cases}
+:<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>
-,-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>
- <!--  -->