Frequency estimation of a complex single-tone in additive white Gaussian noise from irregularly-spaced samples is addressed. In this Letter, we study the periodogram and weighted phase averager, which are standard solutions in the uniform sampling scenarios, for tackling the problem. It is shown that the estimation performance of both approaches can attain the optimum benchmark of the Cramér-Rao lower bound, although the former technique has a smaller threshold signal-to-noise ratio.

In this Letter, the problem of estimating the time-difference-of-arrival between signals received at two spatially separated sensors is addressed. By taking discrete Fourier transform of the sensor outputs, time delay estimation corresponds to finding the frequency of a noisy sinusoid with time-varying amplitude. The generalized weighted linear predictor is utilized to estimate the time delay and it is shown that its estimation accuracy attains Cramér-Rao lower bound.

In this Letter, we explore semi-definite relaxation (SDR) program for finding the real roots of a real polynomial. By utilizing the square of the polynomial, the problem is approximated using the convex optimization framework and a real root is estimated from the corresponding minimum point. When there is only one real root, the proposed SDR method will give the exact solution. In case of multiple real roots, the resultant solution can be employed as an accurate initial guess for the iterative approach to get one of the real roots. Through factorization using the obtained root, the reminding real roots can then be solved in a sequential manner.