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[[Category:ECE301Spring2011Boutin]] | [[Category:ECE301Spring2011Boutin]] | ||
[[Category:problem solving]] | [[Category:problem solving]] | ||
| − | = Practice Question on | + | <center><font size= 4> |
| + | '''[[Signals_and_systems_practice_problems_list|Practice Question on "Signals and Systems"]]''' | ||
| + | </font size> | ||
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| + | [[Signals_and_systems_practice_problems_list|More Practice Problems]] | ||
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| + | Topic: System Properties | ||
| + | </center> | ||
| + | ---- | ||
| + | ==Question== | ||
| + | |||
The input x(t) and the output y(t) of a system are related by the equation | The input x(t) and the output y(t) of a system are related by the equation | ||
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===Answer 2=== | ===Answer 2=== | ||
| − | This system is not causal because the output <math class="inline">y(t)</math> is dependent on future values of t. For any <math class="inline">t_0 \in \Re</math>, the output at <math class="inline">t_0</math>, <math class="inline">y(t_0)</math>, DOES NOT depend only on the input <math class="inline">x(t_0)</math> at <math class="inline">t_0</math> or before <math class="inline">t_0</math>. Meaning <math class="inline"> (t \le t_0)</math> does not hold true because <math>e^t > t</math>. The output will depend on exponentially larger values of <math class="inline"> | + | This system is not causal because the output <math class="inline">y(t)</math> is dependent on future values of <math>x(t)</math> at t. For any <math class="inline">t_0 \in \Re</math>, the output at <math class="inline">t_0</math>, <math class="inline">y(t_0)</math>, DOES NOT depend only on the input <math class="inline">x(t_0)</math> at <math class="inline">t_0</math> or before <math class="inline">t_0</math>. Meaning <math class="inline"> (t \le t_0)</math> does not hold true because <math>e^t > t</math>. The output will depend on exponentially larger values of <math class="inline">t</math>. |
--[[User:Darichar|Darichar]] 13:13, 6 February 2011 (UTC) | --[[User:Darichar|Darichar]] 13:13, 6 February 2011 (UTC) | ||
Latest revision as of 15:22, 26 November 2013
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.
