Strobl22

Applied Harmonic Analysis and Friends

June 19th - 25th 2022

Strobl, AUSTRIA

"Nonlinear time-frequency transforms inspired by audio perception"

Warion, Pierre

The main purpose of this study is to develop time-frequency tools that can integrate aspects related to audio perception. Standard approaches use linear tools such as STFT or the constant Q transform, the latter providing logarithmic frequency precision, which is relevant for modeling audio perception. Starting from the constant Q transform, we develop a new non linear transform which includes (among others) a variance parameter (or scaling effect) that generates an adaptive analysis window. We address two situations : a frequency dependent variance, and a time dependent variance. We study the mathematical properties of the associated time-frequency transforms: in particular we show norm control properties for suitable choices of the analysis window and the time or frequency dependent variance, by introducing kernels and several other analysis tools (approach by stairs functions, admissibility conditions...). A main goal is to develop a well defined approach for inverting such nonlinear time-frequency transforms.

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