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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.
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