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Signal Energy

  1. Aug 18, 2010 #1
    1. The problem statement, all variables and given/known data

    Sketch the signal:
    x(t) = 2^(-t*u(t)) over (-1 < t < 1)

    3. The attempt at a solution
    Attached is an excel fine with my work out. I want to know is it is correct.
     

    Attached Files:

  2. jcsd
  3. Aug 19, 2010 #2
    It is simplest to think of this as a piecewise function
    [tex] x(t) = \begin{cases}
    1, t < 0 \\
    2^{-t}, t>0
    \end{cases}[/tex]
    then
    [tex] x(t)^2 = \begin{cases}
    1, t < 0 \\
    2^{-2t}, t>0
    \end{cases}[/tex]
    so when you integrate x(t)^2 from -1 to 1, it breaks apart into two integrals. One is from -1 to 0 of 1, and the other is from 0 to 1 of 2^{-2t}.
     
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