A pulse amplitude modulation (PAM) signal generator that injects a copy of a pulse into the PAM baseband signal prior to frequency upconversion and power amplification. The pulse comprises a function of, or an extra copy of, a pulse in the PAM baseband signal. The pulse injector analyzes the PAM baseband signal for times when a predetermined threshold is exceeded and forms a pulse that is constructed and arranged to reduce the amplitude of the PAM baseband signal to a desired peak amplitude when the pulse is added to the PAM baseband signal. In other embodiments the peak-to-RMS amplitude ratio reducing methods and apparatus used to process PAM signal are adapted for reducing peak-to-RMS amplitude ratios of amplitude modulation signals in polar modulation transmitters. Peak-to-RMS amplitude ratio reduction is performed in the quadrature domain, the polar domain, or both the quadrature and polar domains.