Determination of Complex Exponentials, Least Squares and Prediction Methods

摘要

An efficient method for determining a sum of complex exponentials and their complex amplitudes is presented in detail. The principal feature is the application of Lanczos' Progressive Algorithm which eliminates the need for knowing or assuming the number of such quantities in the sum. The method is applicable to appropriate averages of the sampled data also. The algebraic properties of the method of least squares for the linear case are presented and provide the basis for the presentation of the 1-step-ahead prediction for stationary sequences lattice filters and canonical variate analysis. Keywords: Correlation analysis.