Fourier transform

kbrijesh · Sep 21, 2012

how to get the fourier transform of (1+at^2)^-n ? n is a natural number such that (n>1) and a is any positive number.

i.e. ∫((1+at^2)^-n)*exp(-jωt)dt; limits of integration goes from -∞ to ∞

jackmell · Sep 21, 2012

kbrijesh said: ↑

how to get the fourier transform of (1+at^2)^-n ? n is a natural number such that (n>1) and a is any positive number.

i.e. ∫((1+at^2)^-n)*exp(-jωt)dt; limits of integration goes from -∞ to ∞

You can do it via contour integration for specific small n but not sure for general n. But first, look at a simple case:

[tex]\int_{-\infty}^{\infty} \frac{e^{-i\omega t}}{(1+2t^2)^2}dt[/tex]

Now that can be solved by the Residue Theorem. First get that one straight, then go on to n=3, maybe 4, then try and come up with an expression for the general case.

kbrijesh · Sep 24, 2012

jackmell said: ↑

You can do it via contour integration for specific small n but not sure for general n. But first, look at a simple case:

[tex]\int_{-\infty}^{\infty} \frac{e^{-i\omega t}}{(1+2t^2)^2}dt[/tex]

Now that can be solved by the Residue Theorem. First get that one straight, then go on to n=3, maybe 4, then try and come up with an expression for the general case.

Yes, you are true. Even using contour integration we can do it upto n=3. But I am y\trying to get a generalized solution.

Anyway, thanks for your reply.

Log in or Sign up

Fourier transform

kbrijesh

jackmell

kbrijesh