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| − | + | <h1> Practice Question on System Invertibility </h1> | |
| − | + | <p>The input x(t) and the output y(t) of a system are related by the equation | |
| − | + | </p><p><span class="texhtml"><i>y</i>(<i>t</i>) = <i>x</i>(<i>t</i> + 2)</span> | |
| − | The input x(t) and the output y(t) of a system are related by the equation | + | </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. |
| − | + | </p> | |
| − | < | + | <hr /> |
| − | + | <h2> Share your answers below </h2> | |
| − | 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>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> | |
| − | + | <hr /> | |
| − | 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! | + | <h3> Answer 1 </h3> |
| − | + | <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> | |
| − | + | </p><p>Proof: | |
| − | Yes, this system is invertible. | + | </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" /> |
| − | + | </p><p>--<a href="User:Cmcmican">Cmcmican</a> 17:08, 24 January 2011 (UTC) | |
| − | Proof: | + | </p><p><br /> |
| − | + | </p> | |
| − | < | + | <dl><dd>Good job! For some reason, this is a problem that a lot of students get stuck on. -pm |
| − | + | </dd></dl> | |
| − | -- | + | <p><br /> |
| − | + | </p><p><br /> | |
| − | + | Why does z(t)=y(t-2)? | |
| − | = | + | </p> |
| − | Write it here. | + | <h3> Answer 2 </h3> |
| − | + | <p>Write it here. | |
| − | Write it here. | + | </p> |
| − | + | <h3> Answer 3 </h3> | |
| − | + | <p>Write it here. | |
| + | </p> | ||
| + | <hr /> | ||
| + | <p><a href="2011 Spring ECE 301 Boutin">Back to ECE301 Spring 2011 Prof. Boutin</a> | ||
| + | </p><a _fcknotitle="true" href="Category:ECE301Spring2011Boutin">ECE301Spring2011Boutin</a> <a _fcknotitle="true" href="Category:Problem_solving">Problem_solving</a> | ||
Revision as of 11:04, 2 February 2011
Contents
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.
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:
<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" />
--<a href="User:Cmcmican">Cmcmican</a> 17:08, 24 January 2011 (UTC)
- Good job! For some reason, this is a problem that a lot of students get stuck on. -pm
Why does z(t)=y(t-2)?
Answer 2
Write it here.
Answer 3
Write it here.
<a href="2011 Spring ECE 301 Boutin">Back to ECE301 Spring 2011 Prof. Boutin</a>
<a _fcknotitle="true" href="Category:ECE301Spring2011Boutin">ECE301Spring2011Boutin</a> <a _fcknotitle="true" href="Category:Problem_solving">Problem_solving</a>
