Recursive versions of the Levenberg-Marquardt reassigned spectrogram and of the synchrosqueezed STFT

Abstract

In this paper, we first present a recursive implementation of a recently proposed reassignment process called the Levenberg Marquardt reassignment, which allows a user to adjust the slimness of the signal components localization in the time-frequency plane. Thanks to a generalization of the signal reconstruction formula, we also present a recursive implementation of the synchrosqueezed short-time Fourier transform. This approach paves the way for a real-time computation of a reversible and adjustable almost-ideal time-frequency representation.