This paper presents a new simple and accurate frequency estimator of a sinusoidal signal based on the signal autocorrelation function (ACF). Such an estimator was termed as the reformed covariance for half-length autocorrelation (RC-HLA). The designed estimator was compared with frequency estimators well-known from the literature, such as the modified covariance for half-length autocorrelation (MC-HLA), reformed Pisarenko harmonic decomposition for half-length autocorrelation(RPHD-HLA), modified Pisarenko harmonic decomposition for half-length autocorrelation (MPHD-HLA), zero-crossing (ZC), and iterative interpolated DFT (IpDFT-IR) estimators. We determined the samples of the ACF of a sinusoidal signal disturbed by Gaussian noise (simulations studies) and the samples of the ACF of a sinusoidal voltage(experimental studies), calculated estimators based on the obtained samples, and computed the mean squared error(MSE) to compare the estimators. The errorswere juxtaposed with the Cramér–Rao lower bound (CRLB). The research results have shown that the proposed estimator is one of the most accurate, especially for SNR > 25 dB. Then the RC-HLA estimator errors are comparable to the MPHD-HLA estimator errors. However, the biggest advantage of the developed estimator is the ability to quickly and accurately determine the frequency based on samples collected from no more than five signal periods. In this case, the RC-HLA estimator is the most accurate of the estimators tested.
Results of the ab initio molecular dynamics calculations of silicon crystals are presented by means of analysis of the velocity autocorrelation function and determination of mean phonon relaxation time. The mean phonon relaxation time is crucial for prediction of the phonon-associated coefficient of thermal conductivity of materials. A clear correlation between the velocity autocorrelation function relaxation time and the coefficient of thermal diffusivity has been found. The analysis of the results obtained has indicated a decrease of the velocity autocorrelation function relaxation time t with increase of temperature. The method proposed may be used to estimate the coefficient of ther-mal diffusivity and thermal conductivity of the materials based on silicon and of other wide-bandgap semiconductors. The correlation between kinetic energy fluctuations and relaxation time of the velocity autocorrelation function has been calculated with the relatively high coefficient of determination R2 = 0.9396. The correlation obtained and the corresponding approach substantiate the use of kinetic energy fluctuations for the calculation of values related to heat conductivity in silicon-based semiconductors (coefficients of thermal conductivity and diffusivity).