Improved spectral resolution

Two new methods are presented for the estimation of the frequencies of closely spaced complex valued sinusoidal signals in the presence of noise. The most effective method is a computationally efficient method for realization of maximum likelihood or maximum posterior probability estimates of the frequencies. The second method is a class of algorithms for removing some of the deficiencies of present adaptive filtering and correlation-estimation approaches to estimation of frequencies, such as the forward-backward linear prediction method. In both of these new methods one is fitting a signal model to data. In method 1 the data are the observed samples of two complex sinusoids plus noise. In the second method the data are elements of an estimated correlation matrix, or of some of its eigenvectors, obtained from the observed samples.