摘要翻译：
本文回顾了R.a.首先提出的一类仿生对数周期波形。Altes在20世纪70年代用于广义目标描述。后来观察到，这种声纳技术与用于多分辨率分析的小波分解之间有着密切的联系。基于此，我们将原始的Altes波形形式化为一族适合于检测加速时间序列振荡的双曲Chirples。这种形式导致了一个非常灵活的小波集，具有可容许性、正则性、消失矩和时频局部化等理想性质。这些“Altes小波”也促进了尺度不变双曲chirplet变换(HCT)的有效实现。从实际的角度来看，加速接近临界的对数周期振荡可以作为一个初始分叉的指标。这种信号在自然界中比比皆是，通常是复杂系统非线性动力学中相变的前兆。例如，作者的兴趣在于自动检测在金融泡沫和之前的市场崩溃期间的对数周期价格动态现象。然而，本文所提出的方法在诸如机械系统的临界故障预测和电气网络的故障检测等各个领域都有更广泛的应用。除了故障诊断之外，还包括通过通话记录、商业和军用雷达识别动物种类，还有更多。为了说明目的，本报告提出了一个综合应用。
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英文标题：
《The Altes Family of Log-Periodic Chirplets and the Hyperbolic Chirplet
  Transform》
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作者：
Donnacha Daly and Didier Sornette
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最新提交年份：
2018
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分类信息：

一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Signal Processing        信号处理
分类描述：Theory, algorithms, performance analysis and applications of signal and data analysis, including physical modeling, processing, detection and parameter estimation, learning, mining, retrieval, and information extraction. The term "signal" includes speech, audio, sonar, radar, geophysical, physiological, (bio-) medical, image, video, and multimodal natural and man-made signals, including communication signals and data. Topics of interest include: statistical signal processing, spectral estimation and system identification; filter design, adaptive filtering / stochastic learning; (compressive) sampling, sensing, and transform-domain methods including fast algorithms; signal processing for machine learning and machine learning for signal processing applications; in-network and graph signal processing; convex and nonconvex optimization methods for signal processing applications; radar, sonar, and sensor array beamforming and direction finding; communications signal processing; low power, multi-core and system-on-chip signal processing; sensing, communication, analysis and optimization for cyber-physical systems such as power grids and the Internet of Things.
信号和数据分析的理论、算法、性能分析和应用，包括物理建模、处理、检测和参数估计、学习、挖掘、检索和信息提取。“信号”一词包括语音、音频、声纳、雷达、地球物理、生理、（生物）医学、图像、视频和多模态自然和人为信号，包括通信信号和数据。感兴趣的主题包括：统计信号处理、谱估计和系统辨识；滤波器设计；自适应滤波/随机学习；（压缩）采样、传感和变换域方法，包括快速算法；用于机器学习的信号处理和用于信号处理应用的机器学习；网络与图形信号处理；信号处理中的凸和非凸优化方法；雷达、声纳和传感器阵列波束形成和测向；通信信号处理；低功耗、多核、片上系统信号处理；信息物理系统的传感、通信、分析和优化，如电网和物联网。
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一级分类：Physics        物理学
二级分类：Data Analysis, Statistics and Probability        数据分析、统计与概率
分类描述：Methods, software and hardware for physics data analysis: data processing and storage; measurement methodology; statistical and mathematical aspects such as parametrization and uncertainties.
物理数据分析的方法、软硬件：数据处理与存储；测量方法；统计和数学方面，如参数化和不确定性。
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英文摘要：
  This work revisits a class of biomimetically inspired log-periodic waveforms first introduced by R.A. Altes in the 1970s for generalized target description. It was later observed that there is a close connection between such sonar techniques and wavelet decomposition for multiresolution analysis. Motivated by this, we formalize the original Altes waveforms as a family of hyperbolic chirplets suitable for the detection of accelerating time-series oscillations. The formalism results in a remarkably flexible set of wavelets with desirable properties of admissibility, regularity, vanishing moments, and time-frequency localization. These "Altes wavelets" also facilitate efficient implementation of the scale invariant hyperbolic chirplet transform (HCT).   From a practical perspective, log-periodic oscillations with an acceleration towards criticality can serve as indicators of an incipient bifurcation. Such signals abound in nature, often as precursors to phase transitions in the non-linear dynamics of complex systems. For example, the authors' interest lies in automatic detection of the well documented phenomenon of log-periodic price dynamics during financial bubbles and preceding market crashes. However, the methodology presented here is more widely applicable in such diverse domains as prediction of critical failures in mechanical systems, and fault detection in electrical networks. Examples beyond failure diagnostics include animal species identification via call recordings, commercial \& military radar, and there are many more. A synthetic application is presented in this report for illustrative purposes.
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PDF链接：
https://arxiv.org/pdf/1803.02695