Math Is Fun Forum

coolwind

Member

Registered: 2005-10-30

Posts: 30

Fourier transform

Find Fourier transform

x(t)=1/(1+(t/3)^2)

Thank you

Last edited by coolwind (2006-10-13 12:23:59)

All_Is_Number

Member

Registered: 2006-07-10

Posts: 258

Re: Fourier transform

Find Fourier transform

x(t)=1/(1+(t/3)^2

Thank you

SYNTAX ERROR! Missing )

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You can shear a sheep many times but skin him only once.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Fourier transform

Here's some reads on complex integration and stuff.
I need to review way lot b4 I can help...
http://www.math.gatech.edu/~cain/winter99/complex.html

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igloo myrtilles fourmis

fgarb

Member

Registered: 2006-03-03

Posts: 89

Re: Fourier transform

Hi Coolwind. Can you tell us what it is about this problem that you are stuck on? Are you having trouble understanding what the fourier transform is/why it works, or are you having trouble with a specific step in the integration? In principle these problems are straightforward even if the math turns out to be complicated.

coolwind

Member

Registered: 2005-10-30

Posts: 30

Re: Fourier transform

Hi fgarb, this is my communication systems homework.

fgarb

Member

Registered: 2006-03-03

Posts: 89

Re: Fourier transform

Ok. Sounds like you're probably not sure how to start.  Just remember that a fourier transform is a way of changing what variable you're expressing your function in terms of. It is often used to switch variables from "time" to "frequency" (I imagine that's what you're using it for here). Speaking of time, I'm a bit short on it at the moment, so I'm afraid I'll have to hurry this, but the basic approach is to plug into this formula:

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Here the integral is from -infinity to +infinity, f is the function before transforming it, and F is the function after the transformation. It should make sense that the t will have been "integrated away" and you'll only be left with your "frequency", w. Does that make sense?

If you understand that, the only hard part would be to evaluate the integral, which is just calculus, however complicated it may be.