Let an input $x\left ( t \right ) = 2 \sin \left ( 10 \pi t \right ) + 5 \cos \left ( 15 \pi t \right ) + 7 \sin \left ( 42 \pi t \right ) + 4 \cos \left ( 45 \pi t \right )$ is passed through an $\text{LTI}$ system having an impulse response,
$$h\left ( t \right ) = 2\left ( \frac{\sin \left ( 10 \pi t \right )}{\pi t} \right ) \cos \left ( 40 \pi t \right )$$
The output of the system is
- $2 \sin \left ( 10 \pi t \right ) + 5 \cos \left ( 15 \pi t \right )$
- $5 \cos \left ( 15 \pi t \right ) + 7 \sin \left ( 42 \pi t \right )$
- $7 \sin \left ( 42 \pi t \right ) + 4 \cos \left ( 45 \pi t \right )$
- $2 \sin \left ( 10 \pi t \right ) + 4 \cos \left ( 45 \pi t \right )$