(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Express the function plotted in the figure below as a Fourier series.

2. Relevant equations

3. The attempt at a solution

I have the fully worked out solution infront of me and im ok with working out the a_{0}, a_{n}and b_{n}parts but what i want to know is why is the function [tex]\frac{A}{\pi}\left|x\right|[/tex] ?

does the [tex]\frac{A}{\pi}[/tex] part refer to the function between 0 and [tex]\pi[/tex]?

If so what about the function between [tex]\pi [/tex]and[tex] 2\pi[/tex]? do i just leave that out? and why is it only integrated below between 0 and pi?

here is the solution:

[tex]f(x)=\frac{A}{\pi}\left|x\right|[/tex] the function is even therefore [tex]{b_n} =0[/tex]

[tex]{a_0}=\frac{2A}{\pi^2}\int^{\pi}_{0}xdx=\frac{2A}{\pi^2}\left[\frac{x^2}{2}\right]^{\pi}_{0}=A[/tex]

[tex]{a_n}=\frac{2A}{\pi^2}\int^{\pi}_{0}xcos(nx)dx=\frac{2A}{n{\pi^2}}\left[xsin(nx)\right]^{\pi}_{0}-\frac{2A}{n{\pi^2}}\int^{\pi}{0}sin(nx)dx[/tex]

...well you get the idea its taking me too long to type out the entire solution so i will leave it at that.

Can someone also please tell me why there is a [tex]\frac{2A}{\pi^2}[/tex] term on the a_{0}and a_{n}terms and why this is not just [tex]\frac{A}{\pi}[/tex]?

In other words where does the extra [tex]\frac{2}{\pi}[/tex] come from? and how will i know when to put it in?

thanks

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# Homework Help: Fourier series sawtooth wave

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