Continuous boostlet transform and associated uncertainty principles

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. An example of an exponential function highlights the CBT’s adaptability. With applications in radar, communications, audio processing, and seismic analysis, the CBT offers efficient time–frequency resolution, making it ideal for non-stationary and transient signals, and a valuable tool for modern signal processing.

• Publication year

  2025

• Venue

  Computational and Applied Mathematics

• Publication date

  2025-03-21

• Fields of study

  Mathematics, Physics, Computer Science, Engineering

• Identifiers
  DOI 10.1007/s40314-025-03529-9arXiv 2504.03679
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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