# For the system, y (t) = u{x (t)} which of the following holds true?

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For the system, y (t) = u{x (t)} which of the following holds true?

(a) System is Linear, time-invariant, causal and stable

(b) System is time-invariant, causal and stable

(c) System is causal and stable

(d) System is stable

This question was addressed to me in a national level competition.

Asked question is from Region of Convergence topic in section Laplace Transform and System Design of Signals and Systems

by (42.1k points)
Correct answer is (b) System is time-invariant, causal and stable

Best explanation: Let x1(t) = v (t), then y1 (t) = u {v (t)}

Let x2(t) = k v (t), then y2 (t) = u {k v (t)} = k y1 (t)

Hence, non-linear

y1 (t) = u {v (t)}

y2 (t) = u {v (t-t0)} = y1 (t-t0)

Hence, time-invariant

Since the response at any time depends only on the excitation at time t=t0, and not on any further values, hence causal.

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