A General Class of Numerically Reliable Algorithms for the Realization of Truncated Impulse Responses

Abstract

The basic goal of this paper is to show that the problem of impulse response-realization allows a very simple formalism . This formalism generalizes the MBH-statement of the realization problem considerably. In this way it unifies many known algorithms, but it also introduces a wealth of possible new procedures. Moreover the geometric interpretations of the various algorithms and numerical techniques can be easily visualized, allowing to discern their strong and weak points. These ideas motivate appropriate decisions for handling noisy data, which is a major concern when developing programs for real life applications. Algorithms have been developed, using the formulation of this paper and numerically reliable techniques, such as Singular Value Decomposition and Generalized Inverses. They are presented together with a feasability study in a companion paper