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GATE ECE 2008 | Question-10

The impulse response $h(t)$ of a linear time-invariant continuous time system is described by $h(t)=\exp (\alpha t) u(t)+\exp (\beta t) u(-t)$, where $u(t)$ denotes the unit step function, and $\alpha$ and $\beta$ are real constants. This system is stable if

  1. $\alpha$ is positive and $\beta$ is positive
  2. $\alpha$ is negative and $\beta$ is negative
  3. $\alpha$ is positive and $\beta$ is negative
  4. $\alpha$ is negative and $\beta$ is positive
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