Practice Question on "Signals and Systems"

More Practice Problems

Topic: System Properties


The input x(t) and the output y(t) of a system are related by the equation

$ y(t)= x\left( e^{t} \right) \ $

Is the system causal? Justify your answer.

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Answer 1

The system is not causal because as t increases the input gets exponentially larger into the future.


Answer 2

This system is not causal because the output $ y(t) $ is dependent on future values of $ x(t) $ at t. For any $ t_0 \in \Re $, the output at $ t_0 $, $ y(t_0) $, DOES NOT depend only on the input $ x(t_0) $ at $ t_0 $ or before $ t_0 $. Meaning $ (t \le t_0) $ does not hold true because $ e^t > t $. The output will depend on exponentially larger values of $ t $.

--Darichar 13:13, 6 February 2011 (UTC)

Answer 3

Write it here.

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