Why Does My Fourier Transform Magnitude Plot Look Incorrect?

[Oliver2000]

Hallo all,

i have a problem with Fourier analysis and i really hope yoou can help me in this forum. i have been trying to find the reason for my problem since many weeks but i could not.

Well, i have this Equation:s(t) = (1/(4*(Pi*t)^(3/2))) * Exp[-3)/(4*t)]

and i need to find the Fourier Frequency for this funtion and then find the magnitude.
my solution:
i used the software mathematica to do it, so i could plot the function s(t) and then its magnitude using as it is shown in the attached images:

Plot[FourierTransform[(1/(4*(Pi*t)^(3/2)))*Exp[-(3)/(4*t)], t,f] // Abs, {f, 0, 100}]

but the problem that the plot of magnitude should look different. it should look like lowpass filter. i mean, that the frequencies should have high amplitude at the beginning and then they should have lower and lower amplitude.
or maybe i have made something wrong in mathematica which led to this weird result. i hope u can help me
regards

 

[Dr.D]

What makes you so sure that this is a low pass filter? I see no reason to think that it is. Quite likely Mathematica has simply given you a correct result that did not match your preconception.