Suppose I have a function f(u), and define g(s)=int(f(u), u from -inf to s), what is the Fourier transform of this function? I could see it may need some additional conditions, or generalized Fourier transforms, etc. Any thoughts?

# what's the Fourier transform of this function?

Started by ●October 10, 2007

Reply by ●October 10, 20072007-10-10

Wowow wrote:> Suppose I have a function f(u), > > and define g(s)=int(f(u), u from -inf to s), > > what is the Fourier transform of this function? I could see it may > need some additional conditions, or generalized Fourier transforms, > etc. > > Any thoughts? > >Note that f is the derivative of g. Try integration by parts for the Fourier transform of g, to obtain g' = f in the integrand. That should get you a relationship between the Fourier transform of g and that of f. Dale