Continuous Boostlet Transform and Associated Uncertainty Principles
Owais Ahmad, Jasifa Fayaz
连续助推器变换(CBT)是用于分析时空信号,特别是声波场的强大工具。 克服经典小波的限制,CBT利用庞加莱群和各向异性扩张来捕捉自然声学场的稀疏特征。 本文介绍了CBT的数学框架,包括其定义,基本属性和相关的不确定性原理,如海森堡的,对数,皮特的,和纳扎罗夫的不等式。 这些结果阐明了助推域中时间和频率定位之间的权衡。 具有恒定和指数函数的实际示例突出了CBT的适应性。 凭借在雷达、通信、音频处理和地震分析方面的应用,CBT提供灵活的时频分辨率,使其成为非静止和瞬态信号的理想选择,也是现代信号处理的宝贵工具。
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...