Analysis of a simple, effective frequency estimator based on Prony´s method

In a recent paper by Tufts and Fiore (1996) a low-complexity frequency estimator based on Prony´s method was proposed. The estimate is formed from two sample correlations rˆ(L₁) and rˆ(L₂), where 1⩽L₁⩽L₂⩽N-1 and N is the number of samples. For a correct phase unwrapping it is required that L₁ and L₂ are relatively prime. In this paper, a slight modification of the original algorithm is presented, and an expression for its asymptotic variance is derived. It is shown that the error variance is minimized for L₁=3N/5 and L₂=4N/5 for which the quotient of the error variance and the Cramer-Rao bound tends to 25/24≈1.042. Suboptimal settings of L₁ and L₂ are shown to exist, resulting in a lowered SNR-threshold while retaining the asymptotic efficiency. Simulation results which lend support to the theoretical findings are included