2025/06/10 by Pierre Warion, Warion, Pierre, Bruno Torrésani +1
Engineering · Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Electrical engineering #FOS: Mathematics #Machine Fault Diagnosis Techniques #Mathematical Analysis and Transform Methods #Signal Processing (eess.SP) #Stability and Controllability of Differential Equations #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2506.08637
openalex publication_date 2025/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This contribution is a follow-up of a recent paper by the authors on adaptive, non-linear time-frequency transforms, focusing on the STFT based transforms. The adaptivity is provided by a focus function, that depends on the analyzed function or signal, and that adapts dynamically the time-frequency resolution of the analysis. Sticking to the continuous case setting, this work provides new stability results for the transform (stability with respect with the focus function). It also investigates in some details focus functions based upon regularized Rényi entropies and show corresponding continuity results.