Evaluation of accuracy of cross-correlation function estimators obtained by using deterministic and randomized quantizing

Celem artykułu jest analiza wpływu różnych rodzajów kwantowania na dokładność wyznaczania funkcji korelacji wzajemnej sygnałów. Rozważono dwa sposoby kwantowania: kwantowanie deterministyczne oraz randomizowane. Dokonano porównania wyników otrzymanych w obu przypadkach. Badania symulacyjne przeprowadzono z zastosowaniem programu ImeCorr opracowanego w środowisku LabWindows. Badano dokładność estymatorów funkcji korelacji wzajemnej otrzymanych z użyciem przetwornika 3-, 8- i 12-bitowego dla argumentu równego zero.The influence of quantization on the cross-correlation function determination of signals is discussed. The relations for cross-correlation function and its digital estimators are given. A method for evaluating the estimator accuracy is presented. Different types of quantization are considered. The formulas describing the quantization ways and related illustrations are presented. In Figures 1, 2 and 3 deterministic, randomized and pseudo-randomized quantization are shown, respectively. To obtain the simulation results, the program ImeCorr prepared in LabWindows was applied. The 3-, 8- and 12-bits quantizers were taken into account. The research results were compared. In Table 1 the values of the relative bias and the relative standard error are shown. It was observed that for 3-bits quantizers the bias had similar values. For the 8- and 12-bits converters the bias is smaller for the randomized and pseudo-randomized quantizing than for the deterministic one. The randomized and pseudo-randomized quantization is a source of the larger standard error than the deterministic quantization. The standard error is smaller for the pseudo-randomized quantization than for the randomized one