Is it possible to view the Hardy-Littlewood Circle method as the Fourier transform with respect to the Lebesgue measure on [0,1) for an appropriate generating function defined in terms of additive characters and then approximating to it by a product of discrete measures? The suggestion was made in a survey article on Waring's Problem in 2002, but I have not been able to find any references illustrating the idea. How exactly one defines a product of discrete measures and uses it to approximate the integral? Also, does the choice of these discrete measures depend on the geometry of the problem at hand? Is there an article/book that illustrates these concepts?