**Practice Question on "Signals and Systems"**

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.

You will receive feedback from your instructor and TA directly on this page. Other students are welcome to comment/discuss/point out mistakes/ask questions too!

### 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)

### Answer 3

Write it here.