The output of a continuous-time, linear time-invariant system is denoted by \(T\left\{ {x\left( t \right)} \right\}\) where \(x\left( t \right)\) is the input signal. A signal \(z\left( t \right)\) is called eigen-signal of the system , when \(T\left\{ {z\left( t \right)} \right\} = \gamma z\left( t \right)\), 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?

• A. is an eigen-signal but is not
• B. ​\(cos\left( t \right)\;and\;sin\left( t \right)\) are both eigen-signals but with different eigenvalues
• C. \(sin\left( t \right)\) is an eigen-signal but \(cos\left( t \right)\) is not
• D. \(cos\left( t \right)\) and \(sin\left( t \right)\) are both eigen-signals with identical eigenvalues