Comparative performance analysis of some instantaneous frequency estimators

In the analysis and processing of the information received by the sensors, it is important to estimate the parameters quickly and accurately. The instantaneous frequency estimation of a real sinus in noise with very few data samples is an important problem in the field of signal processing. Many frequency estimators have been proposed in the literature for this problem. In this thesis, the frequency estimators derived from the discrete energy separation algorithms (DESA-1a, DESA-1, DESA-2) and the four additional estimators, which are derived from the modified covariance and Prony's methods, are considered. It is assumed that a single snapshot is taken, in which the amplitude, phase and frequency of the sinus are constant. Using a Taylor serial expansion technique, simple and accurate closed statements are derived for the variance of the estimators in the case of a sufficiently high signal-to-noise ratio (SNR). The dependence of the variance expressions obtained on the phase of the sine was examined and critical phase values giving the maximum (worst case) and minimum (best case) variances of the estimators and variance expressions in the worst and best scenarios were obtained. Computer simulations that confirm the theoretical results are presented. The variants of the estimators in the worst and best scenarios were compared with each other. It has been observed that the difference between the maximum and minimum variances of the estimators is at a significant level in a wide frequency band.