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Function whose Fourier transform is Dirac delta

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Thread starter papernuke1
Start date Aug 16, 2014
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Delta Dirac Dirac delta Fourier Fourier transform Function Transform

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5 replies · 2K views

papernuke1

Thread starter
Aug 16, 2014

#1

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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johnqwertyful

Aug 16, 2014

#2

Couldn't you just take the inverse Fourier transform?

ShayanJ

Science Advisor

Insights Author

Aug 16, 2014

#3

http://en.wikipedia.org/wiki/Fourier_transform#Distributions

papernuke1

Aug 16, 2014

#4

johnqwertyful said:

Couldn't you just take the inverse Fourier transform?

Oh! I did that and it's it's a constant function, thanks

johnqwertyful

Aug 16, 2014

#5

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. :)

johnqwertyful

Aug 16, 2014

#6

papernuke1 said:

Oh! I did that and it's it's a constant function, thanks

Yup!

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