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 r/spl circ/(L/sub 1/) and r/spl circ/(L/sub 2/), where 1/spl les/L/sub 1//spl les/L/sub 2//spl les/N-1 and N is the number of samples. For a correct phase unwrapping it is required that L/sub 1/ and L/sub 2/ 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 L/sub 1/=3N/5 and L/sub 2/=4N/5 for which the quotient of the error variance and the Cramer-Rao bound tends to 25/24/spl ap/1.042. Suboptimal settings of L/sub 1/ and L/sub 2/ 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.