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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

  1. $0$
  2. $1$
  3. $2$
  4. $3$
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