(New page: Category:ECE301Spring2011Boutin Category:problem solving = Practice Question on the Definition of a Memoryless System= The input x(t) and the output y(t) of a system are related by...) |
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| − | = 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 1=== | ===Answer 1=== | ||
| − | + | Yes. Since the requirement for a system to be memoryless is that for any time | |
| + | <math class="inline">t_0 \in \Re</math>, <math>y(t_0)</math> depends only on the input <math>x(t_0)</math>. | ||
| + | |||
| + | In other words, since this system is dependent only on current values of t, not future or past values, we say it is a memoryless system. --[[User:Darichar|Darichar]] 14:41, 5 February 2011 (UTC) | ||
| + | :Instructor's comment: Yes, the above definition (first part of the answer) is correct answer. Slight correction for the second part: <br> "In other words, since this system<span style="color:red">'s output </span> is dependent only on <span style="color:red"> the </span> current value of <span style="color:red"> the input</span>, not future or past values, we say it is a memoryless system." -pm, | ||
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| + | Question: Is there a proper way to prove this mathematically? or do we just simply answer in words based on intuition? | ||
===Answer 2=== | ===Answer 2=== | ||
Write it here. | Write it here. | ||
Latest revision as of 15:21, 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)= t^2 x(t) $
Is the system memoryless? 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
Yes. Since the requirement for a system to be memoryless is that for any time $ t_0 \in \Re $, $ y(t_0) $ depends only on the input $ x(t_0) $.
In other words, since this system is dependent only on current values of t, not future or past values, we say it is a memoryless system. --Darichar 14:41, 5 February 2011 (UTC)
- Instructor's comment: Yes, the above definition (first part of the answer) is correct answer. Slight correction for the second part:
"In other words, since this system's output is dependent only on the current value of the input, not future or past values, we say it is a memoryless system." -pm,
Question: Is there a proper way to prove this mathematically? or do we just simply answer in words based on intuition?
Answer 2
Write it here.
Answer 3
Write it here.
