# Homework Help: How to find the fourier transform of exp(-|x|)

1. Nov 17, 2008

### samdawy

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. Nov 17, 2008

### gabbagabbahey

That sounds like a good plan to me ....what do you get when you d that?

3. Nov 17, 2008

### samdawy

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?

4. Nov 17, 2008

### gabbagabbahey

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.

5. Nov 17, 2008

### samdawy

should not |x| for any negative value equal to +x ?

sorry but I am a little bit confused,

6. Nov 17, 2008

### gabbagabbahey

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

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?

7. Nov 17, 2008

### samdawy

Yah, I got it

I really thank you for you clarification