Prony, Pad\'e, and Linear Prediction for Interpolation and Approximation in the Time and Frequency Domain Design of IIR Digital Filters and in Parameter Identification

TL;DR

This paper explores Prony, Padé, and linear prediction methods, demonstrating their underlying unity and extending their applications to IIR digital filter design and parameter identification.

Contribution

It unifies the principles behind Prony, Padé, and linear prediction, and extends their application to the frequency sampling design of IIR filters.

Findings

All three methods are based on the same fundamental principles.

They can be generalized and extended for broader applications.

Effective in designing IIR digital filters using frequency sampling.

Abstract

Model based signal processing or signal analysis or signal representation has a rather different point of view from the more traditional filtering and algorithm based approaches. However, in all of these, the names of Prony, Pad\'e, and linear prediction come up. This note examines these ideas with the goal of showing they are all based on the same principles and all can be extended and generalized. A particular application is the frequency sampling design of IIR digital filters.