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How to find the fourier transform of exp(-|x|)

  1. Nov 17, 2008 #1
    1. The problem statement, all variables and given/known data

    I have been trying to solve the fourier transform of exp(-|x|)


    2. Relevant equations

    Do I need to split the function into two parts with different limits,i.e. the first has a limit from -infinity to zero and the secod from zero to +infinity. Please advise?

    3. The attempt at a solution
     
  2. jcsd
  3. Nov 17, 2008 #2

    gabbagabbahey

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    That sounds like a good plan to me :smile:....what do you get when you d that?
     
  4. Nov 17, 2008 #3
    To be honest, I just assumed the exp(-|x|) is equal to exp(-x) for x between the minus and positive infinity and did the normal integration. Am I in the right track?
     
  5. Nov 17, 2008 #4

    gabbagabbahey

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    Well, |x| is equal to -x for negative values of x isn't it?....And so in the interval -inf to 0, exp(-|x|)=exp(+x)....that is why you need to break the integration into two parts.
     
  6. Nov 17, 2008 #5
    should not |x| for any negative value equal to +x ?

    sorry but I am a little bit confused,
     
  7. Nov 17, 2008 #6

    gabbagabbahey

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    if x is negative, then +x is also negative isn't it?:wink:

    For example, let's look at x=-2...clearly +x=-2 while -x=+2 so |x|=-x in this case since |-2|=2....do you follow?
     
  8. Nov 17, 2008 #7
    Yah, I got it

    I really thank you for you clarification
     
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