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The output of a continuous-time, linear time-invariant system is denoted by $T\left\{x(t)\right\}$ where $x(t)$ is the input signal. A signal $z(t)$ is called eigen-signal of the system $T$, when $T\left\{z(t)\right\}=\gamma z(t)$ where $\gamma$ is a complex number, in general, and is called an eigenvalue of $T$. Suppose the impulse response of the system $T$ is real and even. Which of the following statements is TRUE?

  1. $\cos (t)$ is an eigen-signal but $\sin (t)$ is not
  2. $\cos(t)$ and $\sin(t)$ are both eigen-signals but with different eigenvalues
  3. $\sin(t)$ is an eigen-signal but $\cos(t)$ is not
  4. $\cos(t)$ and $\sin(t)$are both eigen-signals with identical eigenvalues
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