Function whose Fourier transform is Dirac delta

Click For Summary

Discussion Overview

The discussion revolves around the existence of a time domain function whose Fourier transform is the Dirac delta function, specifically focusing on whether this function can represent a single frequency impulse without harmonics. The conversation touches on theoretical aspects of Fourier transforms and their inverses.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions if there exists a time domain function whose Fourier transform is the Dirac delta function without harmonics.
  • Another participant suggests that taking the inverse Fourier transform could provide the answer.
  • A third participant references a Wikipedia page on Fourier transforms, indicating a search for more information.
  • One participant concludes that the inverse Fourier transform of the delta function is a constant function, implying that this resolves the initial question.
  • Another participant agrees with the conclusion that the inverse Fourier transform of the delta function is indeed a constant function, reinforcing the earlier claim.
  • There is a mention of a "chicken-egg problem," suggesting a potential philosophical or conceptual dilemma regarding the relationship between the delta function and the constant function.

Areas of Agreement / Disagreement

While some participants agree on the relationship between the delta function and the constant function, the initial question about the existence of a time domain function remains somewhat contested, as not all aspects of the discussion are resolved.

Contextual Notes

There may be limitations in understanding the implications of the inverse Fourier transform and its relationship to the delta function, as well as the definitions of the functions involved.

papernuke1
Messages
3
Reaction score
0
Is there a time domain function whose Fourier transform is the Dirac delta with no harmonics? I.e. a single frequency impulse
 
Physics news on Phys.org
Couldn't you just take the inverse Fourier transform?
 
johnqwertyful said:
Couldn't you just take the inverse Fourier transform?

Oh! I did that and it's it's a constant function, thanks
 
Shyan said:
That will be the chicken-egg problem!

Not really. The inverse Fourier transform of the delta function is 1. The Fourier transform of 1 is the delta function. Everything is fine. :)
 
papernuke1 said:
Oh! I did that and it's it's a constant function, thanks

Yup!
 

Similar threads

MHB Solving wave equation using Fourier Transform
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Polar Fourier transform of derivatives
  • · Replies 4 ·
Replies
4
Views
3K
High School What Is the Fourier Transform of a Constant?
  • · Replies 3 ·
Replies
3
Views
8K
Undergrad Dirac Delta using Fourier Transformation
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Fourier transforms in Hilbert Space
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Fourier transform of Dirac delta
  • · Replies 3 ·
Replies
3
Views
3K
MHB Dirac Delta and Fourier Series
  • · Replies 2 ·
Replies
2
Views
2K
High School How to calculate the Fourier transform of sin(a*t)*exp(-t/b) ?
  • · Replies 7 ·
Replies
7
Views
3K
Graduate Partial differential equation containing the Inverse Laplacian Operator
  • · Replies 3 ·
Replies
3
Views
3K
Insights What Exactly is Dirac’s Delta Function? - Insight
  • · Replies 33 ·
2
Replies
33
Views
10K