Non-recursive frequency estimation for closely spaced sinusoids

A non-recursive frequency estimator for sinusoids in white noise is described. The proposed "integral equation estimator" (IEE) is found by solving a linear least-squares problem in 3M unknowns, where M is the number of frequencies in the complex signal. Simulation results are presented, which indicate that the IEE performs as well as the maximum likelihood estimate (MLE) even at low signal-to-noise ratios. At high SNR, both estimators approach the Cramer-Rao bound. The IEE requires considerably less computation than the MLE and is far easier to implement. Extensions of the method to non-uniform sampling, damped sinusoids, and multi-dimensional spectral estimation are discussed.