phase modulating a filtered baseband signal with a quadrature modulator to generate a passband signal, wherein the passband signal has an amplitude and a phase;

limiting the amplitude of the passband signal with a limiter to generate a limited passband signal;

filtering the limited passband signal with a phase-locked loop (PLL) to generate an output signal and thereby introducing a PLL group delay; filtering a baseband signal with a baseband filter to generate the filtered baseband signal, wherein the baseband filter introduces a baseband-filter group delay, and wherein the baseband- filter group delay compensates for the PLL group delay; wherein the output signal is used by a polar transmitter to generate a transmitted signal, wherein the transmitted signal exhibits an amount of spectral energy at an offset frequency, and wherein the baseband-filter group delay compensates for the PLL group delay such that the amount of spectral energy at the offset frequency is reduced; and further wherein the passband signal has a modulation frequency, wherein the baseband-filter group delay has a maximum value when the modulation frequency is zero Hertz, wherein the PLL group delay has a maximum value when the modulation frequency is a first value, and wherein the maximum value of the baseband-filter group delay is approximately equal to the maximum value of the PLL group delay.