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

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Discussion Overview

The discussion revolves around finding the Fourier transform of the function 1/(1+4t^2). Participants explore various methods and properties related to Fourier transforms, including symmetry, duality, and scaling properties.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant asks how to find the Fourier transform of 1/(1+4t^2).
  • Another suggests using the substitution x=2t along with symmetry or duality properties and scaling property.
  • A different participant proposes expressing the function in terms of an integral involving f(t) = e^{-jωt} and g(t) = 1+4t^2, and mentions a rule involving derivatives of f and g.
  • One participant points out a mix-up between differentiation and integration in the previous suggestion.
  • Another participant expresses that the properties of the Fourier transformation might be a simpler approach.
  • Some participants express confusion about applying the properties of the Fourier transform.
  • There are references to checking the scaling and symmetry properties, but no definitive answers are provided.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best approach to find the Fourier transform, with multiple competing views and methods discussed.

Contextual Notes

Some participants express confusion regarding the application of Fourier transform properties, and there are unresolved aspects regarding the differentiation and integration process mentioned.

kolycholy
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how can I find Fourier transform of 1/(1+4t^2)?
hmmm =/
 
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try to take x=2t and use the symmetry or duality property and then the scaling property
 
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}}
 
Last edited:
antoker said:
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...
 
manchot is right ... so complicated ... i think the properties of the Fourier transformation is better
 
damn... you're right ;)
 
i tried taking a look at the Fourier transform properties..
but hmm, still confused
 
check the scaling and the symmetry property ... sorry i can't tell the answer ... it is the rules ...
 

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