Function whose Fourier transform is Dirac delta

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A time domain function whose Fourier transform is the Dirac delta function is a constant function. The inverse Fourier transform of the Dirac delta yields a constant, confirming that the delta function represents a single frequency impulse. This relationship illustrates the duality between the delta function and constant functions in Fourier analysis. The discussion emphasizes that the Fourier transform of a constant function is indeed the Dirac delta function. Overall, the concepts of Fourier transforms and their inverses are consistent and well-understood in this context.
papernuke1
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Is there a time domain function whose Fourier transform is the Dirac delta with no harmonics? I.e. a single frequency impulse
 
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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!
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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