Find Fourier Transform of 1/1+4t^2

[kolycholy]

how can I find Fourier transform of 1/(1+4t^2)?
hmmm =/

 

[moe_3_moe]

try to take x=2t and use the symmetry or duality property and then the scaling property

 

[antoker]

Use the fact that your expression can be expressed as $$\int{\frac{f(t)}{g(t)}dx}$$, where $$f(t) = e^{-j\omega t}, g(t)=1+4t^{2}$$ and proceed as stated by the rule. If i remember it correctly it goes something like $$\frac{f'(t)g(t)-g'(t)f(t)}{g(t)^{2}}$$

 

[Manchot]

Use the fact that your expression can be expressed as $$\int{\frac{f(t)}{g(t)}dx}$$, where $$f(t) = e^{-j\omega t}, g(t)=1+4t^{2}$$ and proceed as stated by the rule. If i remember it correctly it goes something like $$\frac{f'(t)g(t)-g'(t)f(t)}{g(t)^{2}}$$

You've mixed up differentiation and integration...

 

[moe_3_moe]

manchot is right ... so complicated ... i think the properties of the Fourier transformation is better

 

[antoker]

damn... you're right ;)

 

[kolycholy]

i tried taking a look at the Fourier transform properties..
but hmm, still confused

 

[moe_3_moe]

check the scaling and the symmetry property ... sorry i can't tell the answer ... it is the rules ...