Fourier Transform: Steps to Find the Solution for Given Functions

[myth_kill]

Homework Statement

Homework Equations

i cannot start with the q

The Attempt at a Solution

how to find the Fourier transform of the given function?

i don't want the MATLAB code, i want to know how to actually find the Fourier transform of this function

 

[lanedance]

for starters as its an even function you only need consider cosine terms, and as its periodic only terms with an integer multiple of period will constribute so you will end up with an infinite sum something like
$$f(x) = \sum_n a_n cos(\frac{n \pi x}{ L})$$

to find each coefficient, find the integral over a period of the function multiplied by the corresponding cosine component. This works as the functions are all orthogonal to each other