\fFourier Transforms Writing the exponential function in (9) as a product of exponen- tial functions, we have f(x) = f(v)e du err du (10) The expression inside the brackets is a function of w, is denoted by F(w), and is called the Fourier transform of f; writing v = r, we have F(w) = V2T f(x)e-iwadx. (11) By using (11), (10) becomes f(x) = V2 TT F(w)erwadw (12) -00 and is called the inverse Fourier transform of F(w)