The authors present a statistical approach to the analysis of random pulsewidth modulation (RPWM) methods which generate PWM signals by comparing a reference modulating function with random numbers or signals. Such an approach is used to analyze and optimize a new weighted RPWM (WRPWM) method and also a standard trapezoidal RPWM method. The WRPWM scheme combines the advantages of the nondeterministic and deterministic PWM methods by adding some deterministic nature into the nondeterministic RPWM method. Both theoretical and experimental results confirm that the optimized WRPWM method has better spectral performance over the standard RPWM schemes and has attractive features such as the potential of third-harmonic boosting, reduced acoustic noise, and minimal low-order harmonics under an overmodulation condition for electronic drive applications.