Chirplet approximation of band-limited, real signals made easy

TL;DR

This paper introduces hierarchical algorithms for approximating real band-limited signals with Gaussian Chirps, avoiding complex searches and dictionaries, and relying on signal extrema to determine approximation terms.

Contribution

The proposed algorithms provide a simpler, hierarchical approach for Gaussian Chirp approximation that does not depend on matching pursuit or extensive parameter searches.

Findings

Efficient approximation of band-limited signals using Gaussian Chirps.

Algorithms depend on signal extrema, not on complete chirp dictionaries.

Avoids multi-dimensional searches used in previous methods.

Abstract

In this paper we present algorithms for approximating real band-limited signals by multiple Gaussian Chirps. These algorithms do not rely on matching pursuit ideas. They are hierarchial and, at each stage, the number of terms in a given approximation depends only on the number of positive-valued maxima and negative-valued minima of a signed amplitude function characterizing part of the signal. Like the algorithms used in \cite{gre2} and unlike previous methods, our chirplet approximations require neither a complete dictionary of chirps nor complicated multi-dimensional searches to obtain suitable choices of chirp parameters.