Transient Signal Spaces and Decompositions

TL;DR

This paper introduces a new signal analysis algorithm that identifies decay rates and coefficients in transient signals, offering a novel approach compared to existing methods and with practical applications in signal processing.

Contribution

The paper presents a new sequential algorithm for transient signal decomposition that qualitatively compares favorably to existing orthogonal exponential transform techniques.

Findings

Algorithm effectively identifies decay rates and coefficients.

Provides a functional interpretation via monomial approximation.

Useful for extracting information from transient signals.

Abstract

In this paper, we study the problem of transient signal analysis. A signal-dependent algorithm is proposed which sequentially identifies the countable sets of decay rates and expansion coefficients present in a given signal. We qualitatively compare our method to existing techniques such as orthogonal exponential transforms generated from orthogonal polynomial classes. The presented algorithm has immediate utility to signal processing applications wherein the decay rates and expansion coefficients associated with a transient signal convey information. We also provide a functional interpretation of our parameter extraction method via signal approximation using monomials over the unit interval from the perspective of biorthogonal constraint satisfaction.