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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

  1. $2 \sin \left ( 10 \pi t \right ) + 5 \cos \left ( 15 \pi t \right )$
  2. $5 \cos \left ( 15 \pi t \right ) + 7 \sin \left ( 42 \pi t \right )$
  3. $7 \sin \left ( 42 \pi t \right ) + 4 \cos \left ( 45 \pi t \right )$
  4. $2 \sin \left ( 10 \pi t \right ) + 4 \cos \left ( 45 \pi t \right )$
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