Computationally Feasible Frequency Estimates in the Presence of Unknown Phase and Amplitude

摘要

The problem of estimating the angular frequency in a single trigonometric regression function, observed in the presence of correlated noise, can be approached by the method of Least Squares or procedures based on the theory of empirical spectral analysis. For real time applications, such methods generally are prohibitively time consuming. Two simple and consistent frequency estimates are introduced which use at most the first three sample covariances, and derive and compare their large sample distributions. A by-product of the calculations is a precise analysis of the asymptotic behavior of the (inconsistent) technique known in numerical analysis as Prony's method. (Author)