提出新型时频分析工具CBT，更好处理声波等非平稳信号
Continuous Boostlet Transform and Associated Uncertainty Principles
- 基于庞加莱群与各向同性缩放构建新变换
- 揭示时频局部化间的多类不确定性关系
- 适合雷达、音频、地震等瞬态信号分析
连续博斯特变换（CBT）作为一种强大的时空信号分析工具，特别适用于声波场。克服传统小波的局限性，CBT利用庞加莱群和各向同性缩放捕捉自然声场的稀疏特征。本文建立CBT的数学框架，包括定义、基本性质及相关的不确定性原理，如海森堡、对数、皮特和纳扎罗夫不等式。这些结果阐明了在博斯特域中时间与频率局部化之间的权衡。通过常数和指数函数的实际例子展示了CBT的适应性。该方法在雷达、通信、音频处理和地震分析中有广泛应用，提供灵活的时间-频率分辨率，特别适用于非平稳和瞬态信号，是现代信号处理的重要工具。
原文摘要 · Abstract (English)
The Continuous Boostlet Transform (CBT) is introduced as a powerful tool for analyzing spatiotemporal signals, particularly acoustic wavefields. Overcoming the limitations of classical wavelets, the CBT leverages the Poincaré group and isotropic dilations to capture sparse features of natural acoustic fields. This paper presents the mathematical framework of the CBT, including its definition, fundamental properties, and associated uncertainty principles, such as Heisenberg's, logarithmic, Pitt's, and Nazarov's inequalities. These results illuminate the trade-offs between time and frequency localization in the boostlet domain. Practical examples with constant and exponential functions highlight the CBT's adaptability. With applications in radar, communications, audio processing, and seismic analysis, the CBT offers flexible time-frequency resolution, making it ideal for non-stationary and transient signals, and a valuable tool for modern signal processing.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。