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Induction motor drives operated with a low ratio of the switching frequency to the fundamental frequency (i.e., pulse number) are prone to have high magnitudes of low-order torque harmonics. This paper proposes a method to analytically evaluate the harmonic torque spectrum based on the pulsewidth-modulated voltage waveforms for low pulse number operation. The predicted torque harmonic spectra for different pulsewidth-modulated waveforms are validated through simulations and experiments. This paper also reports optimal switching angles to minimize the total rms value of torque harmonics of order 6, 12, 18 $,\dots,$ $6(N-1)$ , considering the number of switching angles per quarter ($N$) to be 4 and 5. Compared to sine triangle pulsewidth modulation and selective harmonic elimination pulsewidth modulation with the same pulse number, the proposed optimal switching angles significantly reduce the total rms value of all harmonic torques of order lower than $6N$. Extensive simulation and experimental results on a 3.7-kW induction motor drive are presented to demonstrate the superior performance of the proposed optimal pulsewidth modulation. [ABSTRACT FROM AUTHOR]