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Cascade a time delay and a time scaling
Consider the following two systems:
$ x(t) \rightarrow \left[ \begin{array}{ccc} & & \\ & \text{system 1} & \\ & & \end{array}\right] \rightarrow y(t)=x(t+2) $
$ x(t) \rightarrow \left[ \begin{array}{ccc} & & \\ & \text{system 2} & \\ & & \end{array}\right] \rightarrow y(t)=x(5t) $
Obtain a simple expression for the output of the following cascade:
$ x(t) \rightarrow \left[ \begin{array}{ccc} & & \\ & \text{system 1} & \\ & & \end{array}\right] \rightarrow \left[ \begin{array}{ccc} & & \\ & \text{system 2} & \\ & & \end{array}\right] \rightarrow y(t) $
- (Sorry, I don't know how to make a real "box" to represent a system. If somebody knows, please help. -pm)
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
$ x(t) \rightarrow \left[ \begin{array}{ccc} & & \\ & \text{system 1} & \\ & & \end{array}\right] \rightarrow \left[ \begin{array}{ccc} & & \\ & \text{system 2} & \\ & & \end{array}\right] \rightarrow y(t) = x(5(t + 2)) = x(5t + 10) $ --Cmcmican 16:05, 15 January 2011 (UTC)
- Instructors comments: Unfortunately, the answer is not correct. (I actually expected that mistake to happen. Almost everybody does it the first time.) Try to carefully write the output after each step of the cascade, and change the variable explicitely. -pm
Answer 2
$ x(t) \rightarrow \left[ \begin{array}{ccc} & & \\ & \text{system 1} & \\ & & \end{array}\right] \rightarrow \left[ \begin{array}{ccc} & & \\ & \text{system 2} & \\ & & \end{array}\right] \rightarrow y(t) = x(5t + {2 \over {5}}) $
--Rgieseck 11:47, 18 January 2011 (UTC)
Draw an example signal and apply the systems graphically to logically deduce this answer.
Answer 3
write it here.
