I have a graph for a function $f(x)$:
If I have the fourier series representation of the function, is it possible for me to obtain the fourier coefficients without actually having to calculate them? Would I be able to do this using the graph and the representation I have?
$$f(x) = a_0 + \sum_{n=1}^{\infty} \left( a_n\cdot \cos(nx) + b_n \cdot \sin(nx) \right)$$
Even if we can't obtain the exact value of the coefficients I think we have enough to at least determine if any of the coefficients ($a_0, a_n$ or $b_n$) are equal to $0$?
I'm just wondering if this is possible