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Laplace transforms be converted to fourier transforms?

  1. Aug 23, 2009 #1
    can equations involving laplace transforms be converted to fourier transforms?
     
  2. jcsd
  3. Aug 23, 2009 #2

    Tom Mattson

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    Re: transforms

    Fourier transforms are special cases of Laplace transforms. In the Laplace transform you typically start with a function [itex]f(t)[/itex] and transform it to a function [itex]F(s)[/itex], where [itex]s[/itex] is a complex variable. For definiteness: [itex]s=\sigma + i\omega[/itex], [itex]\sigma ,\omega\in\mathbb{R}[/itex]. Let [itex]\mathcal{F}[/itex] denote Fourier transformation and let [itex]\mathcal{L}[/itex] denote Laplace transformation.

    Then:

    [tex]\mathcal{F}[f(t)]=\mathcal{L}[f(t)]|_{\sigma =0}[/tex]
     
  4. Aug 25, 2009 #3
    Re: transforms

    are fourier transforms defined for tan functions as they are defined for sine and cosine
    functions?and where do we use these transforms?
     
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