Inverse fourier transform of constant

[lemonsie]

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)=$\int$ 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.

 

[SammyS]

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)=$\int$ 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?

 

[lemonsie]

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 ∞

 

[lemonsie]

ive got it solved now. thanks anyways sammy! :)