The signal $2\cos(2\pi t/3)-\cos(\pi t)$ enters an LTI system with $H(s)=e^s+e^{-s}$. If $C_k$ is the kth exponential Fourier-series coefficient of the output, $C_3$ equals
The input angular frequencies are $2\pi/3$ and π, so their common fundamental is $\omega_0=\pi/3$. The third harmonic is the −cos πt term, whose positive-frequency coefficient is −1/2.
The frequency response at π is $H(j\pi)=e^{j\pi}+e^{-j\pi}=-2$. Multiplying the input coefficient by this value gives $C_3=(-1/2)(-2)=$ **1, B**.
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