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Deriving the fourier transform

  1. Mar 11, 2015 #1
    1. The problem statement, all variables and given/known data

    derive the fourier sine and cosine transforms of $$f(x) = e^{-cx}$$ by using $$e^{iax}=cos(ax)+isin(ax)$$ and computing the integral $$\int_0 ^{\infty} e^{-cx}e^{iax}dx$$.


    2. Relevant equations


    3. The attempt at a solution

    i'm completely clueless, all i did was evaluate what they told me to.

    $$\int_0 ^{\infty} e^{-cx}e^{iax}dx = \int_0 ^{\infty} e^{(ia-c)x}dx$$
    $$= \frac{e^{(ia-c)x}}{ia-c}\Big|_0^{\infty} = \frac{cos(ax)+isin(ax)}{ia-c}\Big|_0^{\infty} =-\frac{1}{ia-c}$$
     
    Last edited: Mar 11, 2015
  2. jcsd
  3. Mar 11, 2015 #2

    mfb

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    2016 Award

    Staff: Mentor

    If you split your last result in imaginary and real part, you can relate it to the integrals in your other thread.
     
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