This article provides a general overview of time-frequency (T-F) reassignment and synchrosqueezing techniques applied to multicomponent signals, covering the theoretical background and applications. We explain how synchrosqueezing can be viewed as a special case of reassignment enabling mode reconstruction and place emphasis on the interest of using such T-F distributions throughout with illustrative examples.

The Kalman filter (KF) has received a huge interest from the industrial electronics community and has played a key role in many engineering fields since the 1970s, ranging, without being exhaustive, trajectory estimation, state and parameter estimation for control or diagnosis, data merging, signal processing, and so on. This paper provides a brief overview of the industrial applications and implementation issues of the KF in six topics of the industrial electronics community, highlighting some relevant reference papers and giving future research trends.

Singular spectrum analysis (SSA) is a signal decomposition technique that aims at expanding signals into interpretable and physically meaningful components (e.g., sinusoids, noise, etc.). This paper presents new theoretical and practical results about the separability of the SSA and introduces a new method called sliding SSA. First, the SSA is combined with an unsupervised classification algorithm to provide a fully automatic data-driven component extraction method for which we investigate the limitations for components separation in a theoretical study. Second, the detailed automatic SSA method is used to design an approach based on a sliding analysis window, which provides better results than the classical SSA method when analyzing nonstationary signals with a time-varying number of components. Finally, the proposed sliding SSA method is compared to the empirical mode decomposition and to the synchrosqueezed short-time Fourier transform, applied on both synthetic and real-world signals.

This letter introduces new chirp rate and instantaneous frequency estimators designed for frequency-modulated signals. These estimators are first investigated from a deterministic point of view, then compared together in terms of statistical efficiency. They are also used to design new recursive versions of the vertically synchrosqueezed short-time Fourier transform, using a previously published method (D. Fourer, F. Auger, and P. Flandrin, “Recursive versions of the Levenberg-Marquardt reassigned spectrogram and of the synchrosqueezed STFT,” in Proc. IEEE Int. Conf. Acoust., Speech Signal Process., Mar. 2016, pp. 4880-4884). This study paves the way to the real-time computation of a time-frequency representation, which is both invertible and sharply localized in frequency.

A complete evaluation of first-order, second-order and mixed derivatives is proposed for both the (log-)magnitude and the phase of a given Short-Time Fourier Transform (STFT), leading to equivalent expressions based on additional STFTs with specific windows. Consequences are drawn in terms of phase-magnitude relationships, resulting in new formulations of time-frequency techniques such as reassignment, as well as new insights in the structure of admissible STFTs in some special cases.