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This paper investigates distortion of an inverter reference waveform generated using a direct look-up (DLT) algorithm. The sources of various distortion components are identified and the implications for application to variable speed drives and grid connected inverters are described. Harmonic and subharmonic distortion mechanisms are analyzed, and compared with experimental results. Analytical methods are derived to determine the occurrence of subharmonics, their number, frequencies and maximum amplitudes. A relationship is established identifying a discrete set of synthesizable frequencies which avoid sub-harmonic distortion as a function of look-up table length and a practical method for calculation of the look-up table indices, based on finite length binary representation, is presented. Real time experimental results are presented to verify the analytical derivations.