Extension of Pencil-of-Functions Method to Reverse-Time Processing with First-Order Digital Filters.

Abstract : In this presentation, the data signal is processed in reverse-time by a cascade of first order digital filters to yield a family of information signals. The Gram matrix of these information signals is shown to contain the essential information on the poles of the signal. The entire procedure of the application of pencil-of-function method is thus noniterative. Examples presented demonstrate (i) noiseworthiness in the representation problem when data are corrupted by noise, and (ii) the effectiveness of the method in the approximation problem. Comparison of the method with the maximum entropy method (or linear predictor) and the Prony method is also included. (Author)