A modulator comprises a polar generation stage that generates an amplitude and phase component of a modulation signal, a differentiator stage that generates a differentiated phase component by differentiating the phase component; and an event detection stage that detects a high bandwidth event by detecting the amplitude component and/or the differentiated phase component meeting an event criterion. An inversion stage generates a modified amplitude component by inverting the amplitude component in response to detecting the high bandwidth event. A phase offset stage generates a modified differentiated phase component by, in response to detecting the high bandwidth event, adding to the differentiated phase component a phase offset having a magnitude of 180° and a sign opposite to a sign of the differentiated phase component. Amplitude and phase modulation stages employ the modified amplitude component and the modified differentiated phase component to respectively modulate the amplitude and frequency of a carrier signal.