Identification of Chirps with Continuous Wavelet Transform

René Carmona (1) , Wen-Liang Hwang (2) , Bruno Torrésani (3)

1 ORFE - Department of Operations Research and Financial Engineering
2 IIS Sinica - Institute of Information Science
3 CPT - Centre de Physique Théorique - UMR 6207

Chirps are signals (or sums of signals) that may be characterized by a local (i.e. time-dependent) amplitude and a local frequency. Time-frequency representations such as wavelet representations are well adapted to the characterization problem of such chirps. Ridges in the modulus of the transform determine regions in the transform domain with a high concentration of energy, and are regarded as natural candidates for the characterization and the reconstruction of the original signal. A couple of algorithmic procedures for the estimation of ridges from the modulus of the (continuous) wavelet transform of one-dimensional signals are described, together with a new reconstruction procedure, using only information of the restriction of the wavelet transform to a sample of points from the ridge. This provides with a very efficient way to code the information contained in the signal.

Domaines: Statistiques [math.ST]; Traitement du signal et de l'image [eess.SP]

René Carmona, Wen-Liang Hwang, Bruno Torrésani. Identification of Chirps with Continuous Wavelet Transform. Anestis Antoniadis, Georges Oppenheim. Wavelets and Statistics, 103, Springer, pp.95-108, 1995, Lecture Notes in Statistics, 978-0-387-94564-4. ⟨10.1007/978-1-4612-2544-7_7⟩. ⟨hal-01304136⟩