Question

Consider two continuous time system $S_1$ and $S_2$ whose responses to a complex exponential input $e^{j10t}$ are given below,

$S_1:e^{j10t}\to e^{j10t}{e}^{-j20}$

$S_2:e^{j10t}\to t{e}^{j10(t-2)-2e^{j10(t-2)}}$

• A. $S_2$ is linear time variant system
• B. $S_1$ is linear time variant system
• C. $S_2$ is non linear time variant system
• D. $S_1$ is linear time invariant system

Answer 1

Answer: (A), (D)

$S_1$ is linear time invariant system

$S_1:e^{j10t}\to e^{j10(t-2)}$

$S_1$can be expressed as

$y\left(t\right)=x(t-2)$

This system is linear time invariant system

$S_2:e^{j10t}\to (t-2)e^{j10(t-2)}$

$S_2$can be expressed as

$y\left(t\right)=(t-2)x(t-2)$

This system is linear time variant system.