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Luna Moon...
Posted: Sat Jul 19, 2008 6:40 pm
Guest
Hi,

I have difficulty in taking fourier transform of a function f(t).

The function f(t) is not integrable. Through analytical analysis, f(t)
behaves asymptotically the same as a*log(t)/t

for t-> +infinity; and f(t) behaves asymptotically the same as b*log(-
t)/t

for t-> -infinity; where "a" and "b" are some constants.

Is there a way to work around this difficulty and get some sort of
fourier transform of this function f(t), possibly

involving extended functions or functions which can only be evaluated
numerically or distribution functions...

Any thoughts?

Thanks a lot!
The World Wide Wade...
Posted: Sat Jul 19, 2008 11:53 pm
Guest
In article
<131d7d00-e89a-4e3c-a272-fa97acc7682c at (no spam) 56g2000hsm.googlegroups.com>,
Luna Moon <lunamoonmoon at (no spam) gmail.com> wrote:

Quote:
Hi,

I have difficulty in taking fourier transform of a function f(t).

The function f(t) is not integrable. Through analytical analysis, f(t)
behaves asymptotically the same as a*log(t)/t

for t-> +infinity; and f(t) behaves asymptotically the same as b*log(-
t)/t

for t-> -infinity; where "a" and "b" are some constants.

Is there a way to work around this difficulty and get some sort of
fourier transform of this function f(t), possibly

involving extended functions or functions which can only be evaluated
numerically or distribution functions...

Any thoughts?

Thanks a lot!

One thing to notice: f appears to be in L^2(R), so has a classical
Fourier transform in L^2(R).
 
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