2018/03/06 by Donnacha Daly, Didier Sornette, Daly, Donnacha +1
Earth and Planetary Sciences · Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #Data Analysis #FOS: Electrical engineering #FOS: Physical sciences #Marine and environmental studies #Signal Processing (eess.SP) #Statistics and Probability (physics.data-an) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1803.02695
openalex publication_date 2018/03/06 · openalex created_date 2022/09/02 · openalex updated_date 2026/07/28
This work revisits a class of biomimetically inspired log-periodic waveforms\nfirst introduced by R.A. Altes in the 1970s for generalized target description.\nIt was later observed that there is a close connection between such sonar\ntechniques and wavelet decomposition for multiresolution analysis. Motivated by\nthis, we formalize the original Altes waveforms as a family of hyperbolic\nchirplets suitable for the detection of accelerating time-series oscillations.\nThe formalism results in a remarkably flexible set of wavelets with desirable\nproperties of admissibility, regularity, vanishing moments, and time-frequency\nlocalization. These "Altes wavelets" also facilitate efficient implementation\nof the scale invariant hyperbolic chirplet transform (HCT).\n From a practical perspective, log-periodic oscillations with an acceleration\ntowards criticality can serve as indicators of an incipient bifurcation. Such\nsignals abound in nature, often as precursors to phase transitions in the\nnon-linear dynamics of complex systems. For example, the authors' interest lies\nin automatic detection of the well documented phenomenon of log-periodic price\ndynamics during financial bubbles and preceding market crashes. However, the\nmethodology presented here is more widely applicable in such diverse domains as\nprediction of critical failures in mechanical systems, and fault detection in\nelectrical networks. Examples beyond failure diagnostics include animal species\nidentification via call recordings, commercial & military radar, and there are\nmany more. A synthetic application is presented in this report for illustrative\npurposes.\n