Performance analysis of some cumulant-based estimators: harmonics in noise

We consider the problem of estimating the parameters of harmonics (with non-random parameters) observed in zero mean (colored/white, Gaussian/non-Gaussian) stationary mixing noise. A new fourth-order moment based non-parametric estimator is introduced, and it is shown that this estimator is superior to the conventional second-order estimator at all SNR's. The variance of the frequency estimator is shown to converge as 1/T/sup 3/; for the harmonic with frequency /spl omega//sub 0/, and amplitude A/sub 0/, the peak amplitude of the normalized fourth-order spectrum is shown to be /spl alpha/(/spl omega//sub 0/)(|A/sub 0/|/sup 2//2/spl sigma//sub /spl upsi///sup 2/+1)/sup 2/ where /spl alpha/(/spl omega//sub 0/) is the local SNR, and /spl sigma//sub /spl upsi///sup 2/ is the noise variance.<<ETX>>