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Region of convergence

  1. Aug 28, 2005 #1
    One more:
    after doing Laplace transform for this:

    [tex] f(t) = e^{(7+5j)t}u(t-1) [/tex]

    where u(t) = 1 for t >= 0 and 0 otherwise;
    so here's what I have:

    [tex]L[f(t)] = \frac {e^{-(s-7-5j)}}{s-7-5j} [/tex]

    so, my reasoning was that it would converge if Re > 7 because that's the value for which exponential would converge. But why exactly do we not care about Im? I know that by Euler's formula, it [tex]e^{jw}[/tex] would just be oscillating but don't I need a condition for denominator of L[f(t)]?
    Thanks for your time and explanation.
    Last edited: Aug 28, 2005
  2. jcsd
  3. Aug 28, 2005 #2


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    It is bad to have denominator of zero.
    Looks like, if Re > 7 strictly (not >=)
    the denominator can't be zero.
  4. Aug 28, 2005 #3
    Thanks for reply.

    yeah, i know, that's what I was asking about: do I need to state a condition for the denominator to exclude a case where it is = 0?

    edit: what are the cases when Re >= or <= some value?
    let's say I have [tex] L[f(t)] = \frac{1}{s-a}[/tex]
    so, region of convergence would be Re >= a or Re > a?

    thanks again.
    Last edited: Aug 28, 2005
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