Variance of the nonlinear least squares estimate of the frequency separation of two complex exponents

Abstract

This work presents the asymptotic expressions for bias and variance of nonlinear least squares estimate of the frequency separation of two complex exponents with additive stationary Gaussian noise. In contrast to the previously published results, we present the analytic expressions that are valid for all values of frequency, including the ones near zero as well as Nyquist frequency. These variation and bias estimates are in agreement with the results of Monte-Carlo simulations.