# Thread: Find Fourier Series Coefficient

1. ## Find Fourier Series Coefficient

Hi everyone,

I want help to calculate the fourier coefficient (fundamental only) of square wave function described in figure attached.

2. ## Re: Find Fourier Series Coefficient

Welcome to the forum! You will find lots of helpful stuff here, and you will find that if you put down what you do know or some kind of attempt then you will be much more likely to get someone to help.

The formula for the Sin components is:
$\displaystyle b_n=\frac 1{\pi}\int^{\pi}_{-\pi}f(x)sin(nx)dx$

so if you only want the fundamental component then

$\displaystyle b_1=\frac 1{\pi}\int^{\pi}_{-\pi}f(x)sin(x)dx=\frac 1{\pi}\int^{2\pi}_{0}f(x)sin(x)dx$

I moved the interval of integration to match your problem better.

Now for your problem f(x) =1, 0 or -1 depending on the interval being considered this gives

$\displaystyle b_1=\frac 1{\pi}\int^{\pi/2}_{0}sin(x)dx-\frac 1{\pi}\int^{3\pi /2}_{\pi}sin(x)dx$

If you solve this integral you will get the magnitude of the fundamental sin component. There will of course be higher order sin components and for this particular problem there will also be cosine components.