Line 5: Line 5:
 
<math>e^{-2jt} \rightarrow linear-system \rightarrow te^{2jt} </math>
 
<math>e^{-2jt} \rightarrow linear-system \rightarrow te^{2jt} </math>
  
From these two transformations we can tell that the system is as below:
+
The input, cos(2t) is equal to <math>\frac{1}{2}(e^{j2t} + e^{-j2t})</math>
 
+
<math>x(t) \rightarrow linear-system \rightarrow y(t) = tx(-t)</math>
+
 
+
Therefore, when the input, x(t) = cos(2t), the output is as follows:
+
 
+
<math>cost(2t) \rightarrow linear-system \rightarrow y(t) = tcos(-2t)</math>
+

Revision as of 09:03, 18 September 2008

Part B: The basics of linearity

$ e^{2jt} \rightarrow linear-system \rightarrow te^{-2jt} $

$ e^{-2jt} \rightarrow linear-system \rightarrow te^{2jt} $

The input, cos(2t) is equal to $ \frac{1}{2}(e^{j2t} + e^{-j2t}) $

Alumni Liaison

Correspondence Chess Grandmaster and Purdue Alumni

Prof. Dan Fleetwood