Maximum-likelihood evaluation of the parameter vector of a sum of harmonic signals

Spectral analysis of temporal processes modeled as sums of a certain number of nondamping real sinewaves and Gaussian noise is an objective in various fields of science and technology. To test a method for determination of ML parameter estimates for the sum of a known number of nondamping real sinewaves in the presence of additive Gaussian white noise, and to obtain information on the quantitative characteristics of the estimates, we ran computer-modeling exercises. The results confirmed the properties of asymptotic nonbiasing and asymptotic efficiency of parameter estimates obtained on the basis of the method and indicated high frequency resolution for the ML procedure.