Computer Study of Quantizer Output Spectra

Several authors have described formulas for calculating the output noise spectrum from a quantizer when the input is a gaussian waveform. References 1 through 4 are characteristic and contain representative bibliographies. Evaluation of the resulting expressions is difficult because they contain multiple infinite sums of terms containing Hermite polynomials whose order increases without limit. Consequently simplifying assumptions are made about the input spectrum and quantizer characteristics, or only a few terms are evaluated and the rest assumed negligible, to get results. This article describes a more fruitful approach in which the Hermite polynomials are evaluated in conjunction with other parts of the expression such that the combination tends to zero as the order increases to infinity. The convergence is slow and many terms are needed to get sufficient accuracy in the noise spectrum. It is possible to get results even when the quantizer is not linear or symmetrical, and for arbitrary input spectrum shapes. 2391