Example 1.  Assume that is periodic with period  ,  i.e.  ,  and is defined by
          for  .  
Find the Fourier polynomial of degree n = 5.  

Solution 1.

We need to define this function individually in each sub-interval.

Now plot the function and the Fourier polynomial.

Remark. Observe that the Fourier polynomial has period  .  

(c) John H. Mathews 2004