Stability estimates for adaptive focused time-frequency transforms

Pierre Warion, Bruno Torresani

Session: General

Keywords: Adaptive time-frequency transforms, time and frequency focus, entropy-based focus functions.

TL;DR: This paper addresses some mathematical questions related to non-linear, adaptive, time-frequency transforms whose time-frequency resolution is adapted to the analyzed signal using an entopy-based criterion.

Abstract: 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.

Submission Number: 64