Methods and apparatus for reducing high-frequency events in polar domain signals. An exemplary method includes first generating an unmodified rectangular-coordinate signal having in-phase (I) and quadrature phase (Q) components that are modulated according to a predetermined modulation scheme. Next a first sample of the unmodified rectangular-coordinate signal is modified based on how close the first sample is to the origin in the complex signal plane and how fast a signal trajectory between the first sample and a subsequent sample changes. Finally, the modified rectangular-coordinate signal is converted to a polar domain signal having amplitude and phase components. By modifying the first sample in this manner, either or both the amplitude and phase components have reduced high-frequency content compared to a polar domain signal that would be generated without the first sample having been first modified.