Question

State whether the given function is even or odd. Then, showing the details of your work, find the Fourier series of the function, with period 2pi. Result should be in closed form. Plot using Octave or Matlab the first few non-zero partial sums for each case.

f(x)=x for -pi/2<x<pi/2

f(x)=pi-x for pi<x<3pi/2

Answer 1

f(x) = x is an odd function since f(-x) is not equal to f(x)=x . So given function is odd function.

We can find the fourier series as shown:

Now for second function