In my cosmology textbook, there is a derivation of the two-point correlation function (assuming statistically homogeneous and isotropic fluctuations). I follow the derivation up to equation (7.8a). However, between (7.8a) and (7.8b), there is a sin(kx)/(kx) function which has been inserted, and I don't understand why it's been added. I think it might have something to do with the fourier transform of a rectangular function being the sinc(x) function, but I'm not sure how rectangular functions are applicable to the context of the correlation function.
Textbook: The Physics of Cosmology, George Efstathiou.