Problem with fourier analysis

In summary, The speaker has a problem with Fourier analysis and is seeking help in the forum. They have tried to find the reason for their problem for several weeks but have not been successful. They have an equation and need to find the Fourier Frequency and magnitude. They used Mathematica to plot the function and its magnitude, but the result does not match their expectations of a low pass filter. They are asking for help in understanding the result.
  • #1
Oliver2000
1
0
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
 

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  • #2
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.
 
  • #3


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.
 

1. What is Fourier analysis?

Fourier analysis is a mathematical technique used to break down a complex signal or function into simpler components that are easier to understand. It is based on the idea that any periodic signal can be represented as a sum of simple sine and cosine waves with different frequencies and amplitudes.

2. What is the purpose of Fourier analysis?

The purpose of Fourier analysis is to help us understand and analyze complex signals or functions by breaking them down into simpler components. This can be useful in a variety of fields, such as signal processing, data compression, and image or sound analysis.

3. What is the difference between Fourier analysis and Fourier transform?

Fourier analysis and Fourier transform are closely related, but they are not the same thing. Fourier analysis is the mathematical technique used to break down a signal into simpler components, while Fourier transform is a mathematical operation that converts a signal from the time domain to the frequency domain.

4. What are some common problems with Fourier analysis?

One common problem with Fourier analysis is aliasing, which occurs when the frequency of a signal is incorrectly identified due to insufficient sampling. Another problem is spectral leakage, where energy from one frequency leaks into neighboring frequencies, causing distortion in the analysis.

5. How is Fourier analysis used in real-world applications?

Fourier analysis has a wide range of applications, including signal processing, image and sound analysis, data compression, and even in solving differential equations. It is also used in fields such as astronomy, seismology, and medical imaging to analyze and understand complex data.

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