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Calculating coherence time

  1. Jan 19, 2014 #1
    1. The problem statement, all variables and given/known data

    I have the complex term [itex]g(t) = e^{\frac{-|t|}{t_c}}[/itex] which is the degree of the coherence.


    2. Relevant equations

    Now I want to verify that:

    [itex]t_c = \int_{-\infty}^\infty \! |g(t)|^2 \, dt [/itex]


    3. The attempt at a solution

    [itex]\int_{-\infty}^\infty \! |g(t)|^2 \, dt = \int_{-\infty}^\infty \! |e^{\frac{-|t|}{t_c}}|^2 \, dt = \int_{-\infty}^\infty \! e^{\frac{-|t|}{t_c}} e^{\frac{|t|}{t_c}} \, dt = \int_{-\infty}^\infty \! 1 \, dt[/itex]

    2 Problems now.

    First: The integral doesn't have a value if I integrate from - infinity to infinity.
    Second: The value of the indefinite integral is t. Not t_c.

    What am I missing here?
     
  2. jcsd
  3. Jan 19, 2014 #2
    You didn't multiply ##e^{-\frac{|t|}{t_c}}## by itself. Instead, the second multiplier misses the negative sign. Check your work carefully and try again evaluating the integral.
     
  4. Jan 19, 2014 #3
    Huh? I'm really missing something here.

    [itex]|z|^2 = z z^*[/itex]

    So if in my case [itex]z = e^{\frac{-|t|}{t_c}}[/itex] then

    [itex]z^* = e^{\frac{|t|}{t_c}}[/itex]

    Or not?
     
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