On convergence between natural and uniform sampling for PWM generation

Pulse width modulation is discussed in a comparator with periodic reference signal setting with the emphasis on distinctions between natural and uniform sampling. Motivated by low generator complexity of natural sampling, the convergence characteristics between natural and uniform sampling of a continuous, finite energy, band-limited signal is investigated. The necessary and sufficient conditions for lossless natural sampling are derived and shown to ensure lossless uniform sampling as well. A geometrical framework is constructed to upper bound the deviation between uniform and natural samples and the corresponding sampling instances. Finally, the relation between deviation energy and oversampling factor is discussed.