(New page: Category:ECE301Spring2011Boutin Category:problem solving = Practice Question on Linearity of a System= The input x(t) and the output y(t) of a system are related by the equation ...) |
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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]] | ||
| + | |||
| + | |||
| + | 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, this system is linear. | ||
| + | |||
| + | If | ||
| + | |||
| + | <math>x_1(t) \to \Bigg[ system \Bigg] \to y_1(t)= \int_{-\infty}^{t} x_1(\tau) d\tau</math> | ||
| + | |||
| + | and | ||
| + | |||
| + | <math>x_2(t) \to \Bigg[ system \Bigg] \to y_2(t)= \int_{-\infty}^{t} x_2(\tau) d\tau</math> | ||
| + | |||
| + | Then | ||
| + | |||
| + | <math>ax_1(t)+bx_2(t) \to \Bigg[ system \Bigg] \to y(t)= \int_{-\infty}^{t} ax_1(\tau)+bx_2(\tau) d\tau = a\int_{-\infty}^{t} x_1(\tau) d\tau\ +\ b\int_{-\infty}^{t} x_2(\tau) d\tau = ay_1(t)+by_2(t)</math> | ||
| + | |||
| + | --[[User:Cmcmican|Cmcmican]] 19:20, 26 January 2011 (UTC) | ||
| + | |||
| + | :<span style="color:green">TA's comment: Excellent!</span> | ||
| + | --[[User:Ahmadi|Ahmadi]] 17:27, 27 January 2011 (UTC) | ||
===Answer 2=== | ===Answer 2=== | ||
Write it here. | Write it here. | ||
Latest revision as of 15:23, 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)=\int_{-\infty}^t x(\tau) d\tau . \ $
Is the system linear (yes/no)? 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, this system is linear.
If
$ x_1(t) \to \Bigg[ system \Bigg] \to y_1(t)= \int_{-\infty}^{t} x_1(\tau) d\tau $
and
$ x_2(t) \to \Bigg[ system \Bigg] \to y_2(t)= \int_{-\infty}^{t} x_2(\tau) d\tau $
Then
$ ax_1(t)+bx_2(t) \to \Bigg[ system \Bigg] \to y(t)= \int_{-\infty}^{t} ax_1(\tau)+bx_2(\tau) d\tau = a\int_{-\infty}^{t} x_1(\tau) d\tau\ +\ b\int_{-\infty}^{t} x_2(\tau) d\tau = ay_1(t)+by_2(t) $
--Cmcmican 19:20, 26 January 2011 (UTC)
- TA's comment: Excellent!
--Ahmadi 17:27, 27 January 2011 (UTC)
Answer 2
Write it here.
Answer 3
Write it here.
