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Diffuse nonthermal gas discharges generated at atmospheric pressure have found increasing applications in many key materials processing areas such as etching, deposition, and structural modification of polymeric surfaces. To facilitate tailored and improved applications of these novel gas plasmas, we consider their pulsed generation based on one-dimensional numerical simulation of helium-nitrogen discharges. We consider four waveforms of the plasma-generating voltage, namely: 1) sinusoidal; 2) peak-levelled sinusoidal; 3) peak-levelled and tail-trimmed sinusoidal; and 4) pulsed with a Gaussian-shaped tail, all at the same repetition frequency of 10 kHz. For each case, voltage and current characteristics are calculated and then used to assess whether the generated plasma is diffuse and nonthermal. Densities of electrons, ions, and metastables are calculated, together with the dissipated electric power in the plasma bulk. It is found that plasma pulsing can significantly reduce the electric power needed to sustain diffuse nonthermal atmospheric plasmas. Specifically by choosing appropriate pulse shape, the plasma-sustaining power can be reduced by more than 50% without reducing densities of electrons, ions, and metastables. On the other hand, electron density can be enhanced by 68% with the same input electric power if the pulsewidth is suitably narrowed.