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

Correct Answer is : cos(t) and sin(t) are both eigen-signals with identical eigenvalues

\cos (t) is an eigen-signal but \sin (t) is not

\cos (t) \:and\:\sin (t) are both eigen-signals but with different eigenvalues

\sin (t) is an eigen-signal but \cos (t) is not

\cos (t) and \sin (t) are both eigen-signals with identical eigenvalues

GATE Electrical Engineering (EE) 2016 Shift 1 Solved Paper

Question : 45 of 65

Marks: +1, -0

The output of a continuous-time, linear time-invariant system is denoted by

T \{x (t) \}

where

x (t)

is the input signal. A signal

z (t)

is called eigen-signal of the system , when

T \{z (t) \} = γ z (t)

, where

γ

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?

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