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<h1> Practice Question on System Invertibility </h1>
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[[Category:ECE301Spring2011Boutin]]
<p>The input x(t) and the output y(t) of a system are related by the equation  
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[[Category:problem solving]]
</p><p><span class="texhtml"><i>y</i>(<i>t</i>) = <i>x</i>(<i>t</i> + 2)</span>  
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= Practice Question on System Invertibility=
</p><p>Is the system invertible (yes/no)? If you answered "yes", find the inverse of this system. If you answered "no", give a mathematical proof that the system is not invertible.  
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The input x(t) and the output y(t) of a system are related by the equation  
</p>
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<hr />
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<math>y(t)=x(t+2)</math>
<h2> Share your answers below </h2>
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<p>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!  
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Is the system invertible (yes/no)? If you answered "yes", find the inverse of this system. If you answered "no", give a mathematical proof that the system is not invertible.  
</p>
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----
<hr />
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==Share your answers below==
<h3> Answer 1 </h3>
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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!
<p>Yes, this system is invertible. The inverse is <span class="texhtml"><i>y</i>(<i>t</i>) = <i>x</i>(<i>t</i> − 2)</span>  
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</p><p>Proof:  
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===Answer 1===
</p><p><img _fckfakelement="true" _fck_mw_math="x(t) \to \Bigg[ system 1 \Bigg] \to y(t) = x(t+2) \to \Bigg[ inverse \Bigg] \to z(t) = y(t-2) = x((t-2)+2) = x(t)" src="/rhea/images/math/1/d/2/1d2b4d20bda40bd829d0f153b098d096.png" />  
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Yes, this system is invertible. The inverse is <math>y(t)=x(t-2)</math>
</p><p>--<a href="User:Cmcmican">Cmcmican</a> 17:08, 24 January 2011 (UTC)  
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</p><p><br />
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Proof:
</p>
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<dl><dd>Good job! For some reason, this is a problem that a lot of students get stuck on. -pm
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<math>x(t) \to \Bigg[ system 1 \Bigg] \to y(t) = x(t+2) \to \Bigg[ inverse \Bigg] \to z(t) = y(t-2) = x((t-2)+2) = x(t)</math>
</dd></dl>
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<p><br />
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--[[User:Cmcmican|Cmcmican]] 17:08, 24 January 2011 (UTC)
</p><p><br />
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Why does z(t)=y(t-2)?
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:Good job! For some reason, this is a problem that a lot of students get stuck on. -pm
</p>
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===Answer 2===
<h3> Answer 2 </h3>
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Write it here.
<p>Write it here.  
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===Answer 3===
</p>
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Write it here.
<h3> Answer 3 </h3>
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----
<p>Write it here.  
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[[2011_Spring_ECE_301_Boutin|Back to ECE301 Spring 2011 Prof. Boutin]]
</p>
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<hr />
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<p><a href="2011 Spring ECE 301 Boutin">Back to ECE301 Spring 2011 Prof. Boutin</a>
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</p><a _fcknotitle="true" href="Category:ECE301Spring2011Boutin">ECE301Spring2011Boutin</a> <a _fcknotitle="true" href="Category:Problem_solving">Problem_solving</a>
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Revision as of 13:49, 2 February 2011

Practice Question on System Invertibility

The input x(t) and the output y(t) of a system are related by the equation

$ y(t)=x(t+2) $

Is the system invertible (yes/no)? If you answered "yes", find the inverse of this system. If you answered "no", give a mathematical proof that the system is not invertible.


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 invertible. The inverse is $ y(t)=x(t-2) $

Proof:

$ x(t) \to \Bigg[ system 1 \Bigg] \to y(t) = x(t+2) \to \Bigg[ inverse \Bigg] \to z(t) = y(t-2) = x((t-2)+2) = x(t) $

--Cmcmican 17:08, 24 January 2011 (UTC)

Good job! For some reason, this is a problem that a lot of students get stuck on. -pm

Answer 2

Write it here.

Answer 3

Write it here.


Back to ECE301 Spring 2011 Prof. Boutin

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