Question

A system have input x(t) and output y(t) follow following relations
$y\left(t\right)=\{\begin{array}{cc}0x\left(t\right)<0& \\ x\left(t\right)+x(t-2)x\left(t\right)\ge 0& \end{array}$

Then select the correct statements about system.

• A. System is time variant
• B. System is stable
• C. System is memory less
• D. System is causal

Answer 1

Answer: (B), (D)

System is causal

(a) System has memory since the values of the output signal y(t) at time t depends on the present and past input signal x(t).
(b) System is causal since the present output y(t) at time ${}^{\prime }t{}^{\prime }$ depends on the present and past values of the input signal x(t).
(c) System is time - invariant .
(d) System is stable.
${\int }_{-\infty }^{\infty }|y\left(t\right)|<\infty$