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Signal Energy

  1. Oct 12, 2011 #1
    Hi All,

    I am confused about what is meant in the mathematical definition for the energy of a signal. Why is it the integral of the magnitude of the signal squared?

    ∫(|f(t)|^2)

    How do I deal with the absolute value sign? I do not have much experience with absolute value signs in integrals. I did do a search but am still confused. How do I even know if a function will need to be readjusted according to the absolute value sign and, if so, how do I rewrite the function so that it obeys the absolute value condition?
     
  2. jcsd
  3. Oct 12, 2011 #2

    AlephZero

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    If [itex]f(t)[/itex] is a real-valued function the absolute values just "go away", because [tex]|f\,|^2 = |f\,| \times |f\,| = f\,{}^2[/tex]
    is always true - it doesn't matter whether [itex]f[/itex] is positive, negative, or zero.

    If [itex]f[/itex] is a complex-valued function and [itex]f(t) = p(t) + i\,q(t)[/itex], then
    [tex]|f\,|^2 = p^2 + q^2[/tex]
     
  4. Oct 12, 2011 #3
    Wow that was so simple. Thanks!
     
  5. Oct 12, 2011 #4

    AlephZero

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    Somebody once said, "There are only two types of math problem: the trivial ones that you know how to solve, and the impossible ones that you don't" :smile:
     
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