(New page: ==A Linear Problem== For a given system, <math>e^{2jt}</math> -> <math>te^{-2jt}</math> and <math>e^{-2jt}</math> -> <math>te^{2jt}</math> What is the system’s response to <math>c...) |
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Latest revision as of 16:09, 18 September 2008
A Linear Problem
For a given system,
$ e^{2jt} $ -> $ te^{-2jt} $
and
$ e^{-2jt} $ -> $ te^{2jt} $
What is the system’s response to $ cos(2t) $?
Answer
As a general answer, this system, for any input, multiplies the input by t and negates the independent variable. Or:
$ x(t) $ -> $ tx(-t) $
So, the system's response to $ cos(2t) $ is:
$ cos(2t) $ -> $ tcos(-2t) $
but, because cosine is an even function, the answer can also be written as:
$ cos(2t) $ -> $ tcos(2t) $
