# Homework Help: How do you find the fourier expansion coefficients?

1. Apr 18, 2017

### Vitani11

1. The problem statement, all variables and given/known data
I need to expand this piecewise function f(x) = h for a<x<L and f(x) = 0 for 0<x<a. I am told that this is a square wave so ao and an in the expansion are 0 (odd function). Therefore I only need to worry about bn. The limits on the integral are from a to L, but what about the coefficient? Is it 1/(L-a)? Also for the sine term which is inside the integrand - is this just (L-a) in replace of the L in the general formula?That's what I did and I want to make sure.
2. Relevant equations
bn = 1/L∫f(x)sin(nπx/L)dx where the limits are from -L to L in general.
I have bn = 1/(L-a)∫hsin(nπx/(L-a))dx where the limits are from a to L.

3. The attempt at a solution
I've found the fourier expansion to be 4hL/π(L-a) ∑sin(nπx/(L-a))

Last edited: Apr 18, 2017
2. Apr 18, 2017

### Ken Miller

It looks like you are stating some things that aren't true, and plugging some values into formulas without really understanding how the formulas work.
First questions:
1) Can you verify for yourself whether this is a square wave? What is the definition of a square wave? Does it matter?
1a) Is this really a square wave? It is a rectangular wave, yes, but square? I think many (most?) would say that a square wave has equal amounts of on/off (high/low, etc.). 1b) Does the answer to 1a) matter?
2) Is this an odd function? Draw it out, and use the definition of odd function.
Odd function means $f(-x)=-f(x)$. How do you know that is odd? It is not obvious from the information you give.