(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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===Answer 1===
 
===Answer 1===
Write it here.
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Yes, this system is linear.
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If
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<math>x_1(t) \to \Bigg[ system \Bigg] \to y_1(t)= \int_{-\infty}^{t} x_1(\tau) d\tau</math>
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and
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<math>x_2(t) \to \Bigg[ system \Bigg] \to y_2(t)= \int_{-\infty}^{t} x_2(\tau) d\tau</math>
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Then
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<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>
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--[[User:Cmcmican|Cmcmican]] 19:20, 26 January 2011 (UTC)
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===Answer 2===
 
===Answer 2===
 
Write it here.
 
Write it here.

Revision as of 15:20, 26 January 2011

Practice Question on Linearity of a System

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.


Share your answers below

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)

Answer 2

Write it here.

Answer 3

Write it here.


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