Understanding Fourier Transforms: Solving Confusion with Even Functions

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Discussion Overview

The discussion revolves around the Fourier Transform of a specific piecewise function defined for |t| < 1 and |t| > 1. Participants are exploring the implications of the function being even and whether this allows for the use of the Fourier cosine transform, as well as addressing confusion arising from differing results in calculations.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant presents a piecewise function f(t) and describes their process of finding its Fourier Transform using the integral of f(t)e^(-iwt).
  • The same participant questions whether the even nature of the function permits the use of the Fourier cosine transform, noting a discrepancy in their results.
  • Another participant confirms that the function is indeed even and suggests that the Fourier cosine transform can be used, but expresses uncertainty about the differing results due to lack of visibility of the original solution.
  • A later reply mentions using the formula for the Fourier cosine transform, indicating a specific approach taken by one participant.
  • There is a side conversation regarding the similarity of usernames between participants, which does not directly relate to the main topic.

Areas of Agreement / Disagreement

Participants generally agree that the function is even and that the Fourier cosine transform can be applied. However, there is disagreement or confusion regarding the differing results obtained by participants, and the discussion remains unresolved regarding the source of this discrepancy.

Contextual Notes

Some limitations include the lack of detailed solutions posted by participants, which prevents a full understanding of the discrepancies in results. The discussion also depends on the definitions and properties of Fourier transforms and even functions.

engcon
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Hi, I got a problem in which I have to find the Fourier Transform of a function f(t) defined:

f(t) = { 1 - |t|, |t| < 1
0, |t| > 1 }

Well , I found the Fourier transform by working out the integral f(t)e^(-iwt) with the limits being -inf to +inf (and I got the right answer).

Now, since f(t) is an even function, does that mean I can use the Fourier cosine transform?

I tried to work it out and got a different answer, and basically I'm confused? :frown:

Any help is appreciated, thanks!
 
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yeah i have the same problem here!
 
Yes, the function is even, and so you can use the Fourier cosine transform. However, since you've not posted your solution, I can't see why you're getting a different answer.

eng_pro said:
yeah i have the same problem here!

Your user-name is very similar to the OP's. Coincidence?
 
yes i did it

i used: Fcosine = 2*int (1-t) cos (wt) dt from 0 to1
 
yep it is coincidence..i don't know the OP's username k
 

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