A novel approach to the description of flame transfer functions of premixed swirling flames is presented based on a simplified analysis of the vorticity transport equation. With this model it is possible to reproduce transfer function amplitude in excess of unity observed for swirling flames as well as to explain the differences seen in flame transfer functions for different swirler types. Measurements of flame transfer functions were performed on perfectly premixed flames generated by an axial and a radial swirler with an annular exit. Flames were adjusted as to achieve respective dynamic similarity. The comparison of the flame transfer functions shows the influence of the swirler type. Good agreement with the model validates the theoretical approach and allows to attribute the specific differences seen between the two swirler types with the generation of a swirl number modulation induced by the convective time delay between radial swirler and burner exit. The model also allows to explain the change of flame transfer function amplitude with pre-heating observed in previous publications.