An iterative method for exact maximum likelihood estimation of the parameters of a harmonic series

A procedure is described for determining the exact maximum-likelihood (ML) estimates of the parameters of a harmonic series (i.e. the fundamental frequency, and the amplitude and phase of each harmonic). Existing ML methods are only approximate in the sense that terms present due to mixing between the harmonics are ignored; these terms asymptotically reduce to zero as the sample size increases to infinity. It is argued that these terms can be significant for short signal lengths. The application of the expectation-maximization algorithm results in an iterative procedure that converges to a stationary point on the true parameter likelihood surface. If global convergence results, this point yields the exact ML estimates. Simulation studies illustrate the advantages of the method when short data lengths are used