I am trying to find f(x,y), which can be obtain by doing the backward Fourier integral to F(\omega_x, \omega_y). I have 2 questions.

1. Is there any Fortran code that could evaluate the (numerical) Fourier integral?

2. Since the function f(x,y) is 2-dimensional, we have to do a double integral. Suppose that we evaluate first the x-integral. I have a polynimial in the denominator, but the roots of the polynomial will be functions of y. Then, how can I tell if the (simple) poles are in the upper half plane or not?