I have the following problem:
I must Determine the real Fourier coefficients for the nodes $x_k = \frac{2πk}{4} , k ∈{0, 1, 2, 3}$ for the following function
$f(x) = \left\{\begin{matrix} &-1 & 0 ≤ x < π\\ & 1 & π ≤ x ≤ 2π \end{matrix}\right. $
and give the corresponding Fourier transformatiomn $f_F:[0,2π]→R$ explicitly.
I really don't know how to find the Fourier coefficients.
Can someone help me? and from them how can I find the Fourier transformation?