Inverse fourier transform of constant

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Homework Statement


Find the inverse fourier transform of f(w)=1 Hint: Denote by f(x) the inverse fourier transform of 1 and consider convolution of f with an arbitrary function.


Homework Equations



From my textbook the inverse fourier transform of f(w)=[itex]\int[/itex] F(w)e^-iwt dw


The Attempt at a Solution



Ive tried letting f(x) be the fourier transform of 1 and convolving it with an arbitrary function g(x) but for some reason this leads me nowhere.
 

Answers and Replies

  • #2
SammyS
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Homework Statement


Find the inverse fourier transform of f(w)=1 Hint: Denote by f(x) the inverse fourier transform of 1 and consider convolution of f with an arbitrary function.


Homework Equations



From my textbook the inverse fourier transform of f(w)=[itex]\int[/itex] F(w)e^-iwt dw


The Attempt at a Solution



I've tried letting f(x) be the Fourier transform of 1 and convolving it with an arbitrary function g(x) but for some reason this leads me nowhere.
Precisely what sort of nowhere do you get to?
 
  • #3
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i let f(x)= Inverse fourier transform of 1, which from the formula i have gives f(x)=∫e^-iwx dw

then using the convolution formula with my f(x) above and the aribitrary function g(x) i get

f*g(x) = ∫e^-iwx dw ∫ g(x-t) dt

the integrals have bounds -∞ to ∞
 
  • #4
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ive got it solved now. thanks anyways sammy! :)
 

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