The goal of our scattering experiments is to derive the distribution the differential cross-section and elucidate the dynamics of a bimolecular collision via pure rotational spectroscopy. We have explored the use of a data reduction model to directly transform rotational line shapes into the differential cross section and speed distribution of a reactive bimolecular collision. This inversion technique, known as Fourier Transform Doppler Spectroscopy (FTDS), initially developed by James Kinsey, deconvolves the velocity information contained in one-dimensional Doppler Profiles to construct the non-thermal, state-selective three-dimensional velocity distribution. By employing an expansion in classical orthogonal polynomials, the integral transform in FTDS can be simplified into a set of purely algebraic expressions technique; i.e. the Taatjes method. In this investigation, we extend the Taatjes method for general use in recovering asymmetric velocity distributions. We have also constructed a hypothetical asymmetric distribution from adiabatic scattering in Argon-Argon to test the general method. The angle- and speed-components of the sample distribution were derived classically from a Lennard-Jones 6-12 potential, with collisions at 60 meV, and mapped onto Radon space to generate a set of discrete Doppler profiles. The sample distribution was reconstructed from these profiles using FTDS. Both distributions were compared along with derived total cross sections for the Argon–Argon system. This study serves as a template for constructing velocity distributions from bimolecular scattering experiments using the FTDS inversion technique.