Chirplet approximation of band-limited, real signals made easy

J.M Greenberg (1) , Laurent Gosse (2)

1 Department of Mathematical Sciences [Pittsburgh]
2 IAC - Istituto per le Applicazioni del Calcolo "Mauro Picone"

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.

Mots clés: Chirplet decomposition; Paley-Wiener class; Band limited signals

Domaines: Analyse numérique [math.NA]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

J.M Greenberg, Laurent Gosse. Chirplet approximation of band-limited, real signals made easy. SIAM Journal on Scientific Computing, 2009, 31 (5), pp.3922-3945. ⟨10.1137/080734674⟩. ⟨hal-00323347⟩