Given a probability density function, $f\left(x\right)$, of a continuous random variable, $X$, and given an $N$-th order fourier series approximation:
$$f_N\left(x\right)=\sum_{n=-N}^{N}c_n e^{inx}$$
Is there an upper bound for the truncation error, for an arbitrary $f\left(x\right)$? (given only the assumptions $f\left(x\right) \ge 0$ and $\int_{-\infty}^{\infty}f\left(x\right)\text{d}x=1$)