Numerical Fourier transform

Main Question or Discussion Point

hi, i would need some info on how can implement in MATLAB or FORTRAN (g90) the Numerical evaluation of the integral

$$\int_{-\infty}^{\infty}dxf(x)exp(iux)$$

and the evaluation of the ivnerse Fourier transform

$$\int_{-\infty}^{\infty}du\frac{F(u))}{\int_{-\infty}^{\infty}g(x)exp(iux)dx}$$

the idea is to implement some numerical tool to evaluate Fourier transform integral, in order to apply them to solve Wiener-Hopf equation.