The Altes Family of Log-Periodic Chirplets and the Hyperbolic Chirplet Transform

Daly, Donnacha1; Sornette, Didier2,3,4

2021-10-01

10.3390/sym13101922

SYMMETRY-BASEL   影响因子和分区

2073-8994

This work revisits a class of biomimetically inspired waveforms introduced by R.A. Altes in the 1970s for use in sonar detection. Similar to the chirps used for echolocation by bats and dolphins, these waveforms are log-periodic oscillations, windowed by a smooth decaying envelope. Log-periodicity is associated with the deep symmetry of discrete scale invariance in physical systems. Furthermore, there is a close connection between such chirping techniques, and other useful applications such as wavelet decomposition for multi-resolution analysis. Motivated to uncover additional properties, we propose an alternative, simpler parameterisation of the original Altes waveforms. From this, it becomes apparent that we have a flexible family of hyperbolic chirps suitable for the detection of accelerating time-series oscillations. The proposed formalism reveals the original chirps to be a set of admissible wavelets with desirable properties of regularity, infinite vanishing moments and time-frequency localisation. As they are self-similar, these "Altes chirplets " allow efficient implementation of the scale-invariant hyperbolic chirplet transform (HCT), whose basis functions form hyperbolic curves in the time-frequency plane. Compared with the rectangular time-frequency tilings of both the conventional wavelet transform and the short-time Fourier transform, the HCT can better facilitate the detection of chirping signals, which are often the signature of critical failure in complex systems. A synthetic example is presented to illustrate this useful application of the HCT.

wavelet transform complex systems discrete scale invariance chirping log-periodicity

SCI

英语

通讯

Science & Technology - Other Topics

Multidisciplinary Sciences

WOS:000715603200001

MDPI

Web of Science

1.Lucerne Univ Appl Sci & Arts, Sch Comp Sci & Informat Technol, Suurstoffi 1, CH-6343 Rotkreuz, Switzerland
2.Swiss Fed Inst Technol, Dept Management Technol & Econ, Scheuchzerstr 7, CH-8092 Zurich, Switzerland
3.Southern Univ Sci & Technol SUSTech, Acad Adv Interdisciplinary Studies, Inst Risk Anal Predict & Management, Shenzhen 518055, Peoples R China
4.Tokyo Inst Technol, Inst Innovat Res, Tokyo Tech World Res Hub Initiat WRHI, Tokyo 1528550, Japan

Daly, Donnacha,Sornette, Didier. The Altes Family of Log-Periodic Chirplets and the Hyperbolic Chirplet Transform[J]. SYMMETRY-BASEL,2021,13(10).

Daly, Donnacha,&Sornette, Didier.(2021).The Altes Family of Log-Periodic Chirplets and the Hyperbolic Chirplet Transform.SYMMETRY-BASEL,13(10).

Daly, Donnacha,et al."The Altes Family of Log-Periodic Chirplets and the Hyperbolic Chirplet Transform".SYMMETRY-BASEL 13.10(2021).