Time-frequency analysis on groups

2020/09/16 by Ville Turunen, Turunen, Ville
Computer Science · Engineering · Mathematics · #43A30 (Primary) #47G30 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Sparse and Compressive Sensing Techniques #math.FA #msc:43A30 #msc:47G30

paper · pdf · doi:10.48550/arxiv.2009.08945

44 pages, 4 figures

arxiv created 2020/09/16 · openalex publication_date 2020/09/16 · arxiv updated 2020/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Phase-space analysis or time-frequency analysis can be thought as Fourier analysis simultaneously both in time and in frequency, originating from signal processing and quantum mechanics. On groups having unitary Fourier transform, we introduce and study a natural family of time-frequency transforms, and investigate the related pseudo-differential operators.

Citations

• Generalized Phase-Space Distribution Functions
• Engineering Applications of Noncommutative Harmonic Analysis: With Emphasis on Rotation and Motion Groups
• Quantum mechanics as a statistical theory
• On the Quantum Correction For Thermodynamic Equilibrium

Related

• Time-Frequency analysis via the Fourier Representation
• Characterizing the Fourier transform by its properties
• The abstruse meets the applicable: Some aspects of time-frequency analysis
• Interesting Open Problem Related to Complexity of Computing the Fourier Transform and Group Theory
• A Frequency Space for the Heisenberg Group