Consider the periodic function with period 2 given by
$$ f(x) = 2x, 0 \leq x \leq 1 $$ $$f(x) = 2x -4, 0 < x \leq 2$$
If c_k denote the k-th complex fourier coefficient, we know, using the derivative property, that
$$\bar{c_k} = (i k \omega) c_k$$
But how to use this, in this case, since the derivative is always the constant 2?
Thanks!
(P.S: $c_k = \frac{1}{T} \int_{0}^T f(x) exp(-i k \omega x) dx$)
@Edit
Using the delta function, I think that the correct value of the derivative should be
$$ 2 -4 \sum_{k=- \infty}^\infty \delta (x - 2k+1)$$