Topic: System Properties

## Question

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.

## Share your answers below

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### Answer 1

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

-Mayboch

### 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)

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