Power spectrum of a sigma-delta modulator with hexagonal vector quantization and constant input

A new application of sigma-delta modulation has emerged in soft switching three phase power electronic converters. For this application, a conventional sigma-delta modulator with scalar signals and binary quantizer is generalized to a sigma-delta modulator with vector signals and a truncated hexagonal lattice quantizer. This vector sigma-delta modulator has an interesting output spectrum which is of importance in assessing performance and interpreting results. This paper analytically derives the output spectrum for the case of a generic constant input using ergodic theory and Fourier series on the hexagon.