Study of selected sinusoidal signal characteristic obtained from six signal samples

W artykule przedstawiono wyniki badania własności wybranej charakterystyki sygnału sinusoidalnego wyznaczanej na podstawie możliwie najmniejszej liczby próbek sygnału. Do badań zastosowano funkcję autokorelacji sygnału. Pokazano, że do wyznaczania wartości funkcji autokorelacji wystarczy sześć próbek sygnału oraz, że podczas obliczania wartości funkcji autokorelacji odpowiedni dobór parametrów sygnału powoduje wyeliminowanie skutków operacji kwantowania.This paper presents the results of a research of the selected sinusoidal signal characteristic obtained from the smallest possible number of the signal samples. Research was carried out using the autocorrelation function. It was shown that the values of the autocorrelation function can be determined on the basis of six signal samples. It was also shown that the appropriate selection of the signal parameters eliminates the effects of quantization. Chapter 1 provides basic information on the reasons for study of the autocorrelation function properties. In Chapter 2 the results of the theoretical study were presented. Th. 1 deals with the determination of the sinusoidal signal autocorrelation function and her estimator, when M >> 1, where M is the number of samples. Eq. (1) describes the relation between the number of samples and the delay times of the autocorrelation function. Eq. (3) presents the autocorrelation function estimator. In the second Theorem, it has been shown that, to determine the autocorrelation function values can be used only six sinusoidal signal samples. In the next part of Chapter 2 the third Theorem has been presented. It has been shown that if the initial phase of the signal is equal to (...)/2, then the effects of quantization are eliminated. In Chapter 3 the results of the experimental research were presented. Eq. (22) and (23) describes the mean of the mean square estimator obtained on the basis the autocorrelation function. In Fig. 1 the eq. (22) and (23) have been shown