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This paper presents analytical techniques for the determination of the expressions for the modulation signals used in the carrier-based non-sinusoidal and generalized discontinuous PWM modulation (GDPWM) schemes for two-level, three-phase voltage source inverters. The resulting modulation schemes are applicable to inverters generating balanced or unbalanced phase voltages feeding either star or delta connected loads. The results presented in this paper analytically generalize the several expressions for the modulation signals already reported in the literature. Confirmatory experimental results are provided to illustrate some of the feasible modulation signals.