Biperiodogram frequency estimates: asymptotic and finite sample size

Estimating the frequencies of sinusoidal signals from noisy observations is discussed. In particular it is assumed that the sinusoids are phase coupled. The biperiodogram is used to estimate the frequencies of the phase coupled sinusoids. The mean-square convergence of (modified) biperiodogram frequency estimates is proven. The asymptotic variances of the biperiodogram estimates are shown to be of the same order as the corresponding Cramer-Rao bounds (CRB); however, the asymptotic CRB is not achieved. For the case of equal amplitude sinusoids the asymptotic efficiency of the estimates is 3/8. The finite sample size properties of the biperiodogram estimates are studied through simulations and compared with corresponding periodogram frequency estimates. For small sample size (e.g. N=64) experimental results indicate that better estimates are obtained with the biperiodogram