A signal $2 \cos(\frac{2\pi}{3}t)-\cos(\pi t)$ is the input to an LTI system with the transfer function

$$H(s)=e^s+e^{-s}.$$

If $C_k$ denotes the $k^{th}$ coefficient in the exponential Fourier series of the output signal, then $C_3$ is equal to

- $0$
- $1$
- $2$
- $3$