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.

 

[Mene]

It seems like you are having difficulty understanding the behavior of your function in the frequency domain. This is a common issue in Fourier analysis, as it can be challenging to interpret the results without a strong understanding of the underlying mathematical concepts.

One possible explanation for the unexpected magnitude plot is that your original function has a singularity at t=0, which can affect the behavior in the frequency domain. It is important to carefully consider the properties of your function and its Fourier transform to better understand the results you are seeing.

I would suggest consulting with a mathematics or signal processing expert to help you better understand the behavior of your function and its Fourier transform. They may be able to point out any errors in your approach and provide insights on how to correctly interpret the results.

Additionally, it may be helpful to review the fundamentals of Fourier analysis and familiarize yourself with the properties of different types of signals and their corresponding frequency spectra. This will give you a better understanding of how to interpret the results and identify any potential issues.

I hope this helps and wish you the best of luck in resolving your problem with Fourier analysis.