Finite Sample Correlations of Quantized Gaussians

Abstract

A theory is developed for the treatment of quantized signals and for the estimate of correlation from quantized signals of only finite length. Different quantization systems can be compared on the accuracy of estimation of correlation for the same record length. For Gaussian statistics it is shown that with low values of correlation the efficiencies of one, two, and three bit quantizations are respectively 64, 89, and 95% with respect to continuous multiplication. For highly correlated signals the one bit system becomes the most efficient