A novel technique based on Fourier transform theory has been developed that directly extracts respiratory information from projections without the use of external surrogates. While the feasibility has been demonstrated with three patients, a more extensive validation is necessary. Therefore, the purpose of this work is to investigate the effects of a variety of respiratory and anatomical scenarios on the performance of the technique with the 4D digital extended cardiac torso phantom. FT-phase and FT-magnitude methods were each applied to identify peak-inspiration projections and quantitatively compared to the gold standard of visual identification. Both methods proved to be robust across the studied scenarios with average differences in respiratory phase <10% and percentage of projections assigned within 10% of the gold standard >90%, when incorporating minor modifications to region-of-interest (ROI) selection and/or low-frequency location for select cases of DA and lung percentage in the field of view of the projection. Nevertheless, in the instance where one method initially faltered, the other method prevailed and successfully identified peak-inspiration projections. This is promising because it suggests that the two methods provide complementary information to each other. To ensure appropriate clinical adaptation of markerless, self-sorted four-dimensional cone-beam CT (4D-CBCT), perhaps an optimal integration of the two methods can be developed.