This letter deals with the problem of the estimation of the instantaneous frequencies of the modes of multicomponent signals from their linear time-frequency representations. In most approaches, such an estimation consists of extracting the ridges associated with each mode in the time-frequency plane. A major issue associated with these techniques is that ridge detection relies on some ad-hoc parameters, which essentially bound the modulation of the studied modes and put some constraints on the type of filter used in the time-frequency representation. In this paper, we alternatively propose a novel fully adaptive approach for ridge detection whose relevance is shown throughout numerical simulations.

Modern time series are usually composed of multiple oscillatory components, with time-varying frequency and amplitude contaminated by noise. The signal processing mission is further challenged if each component has an oscillatory pattern, or the wave-shape function, far from a sinusoidal function, and the oscillatory pattern is even changing from time to time. In practice, if multiple components exist, it is desirable to robustly decompose the signal into each component for various purposes, and extract desired dynamics information. Such challenges have raised a significant amount of interest in the past decade, but a satisfactory solution is still lacking. We propose a novel nonlinear regression scheme to robustly decompose a signal into its constituting multiple oscillatory components with time-varying frequency, amplitude and wave-shape function. We coined the algorithm shape-adaptive mode decomposition (SAMD). In addition to simulated signals, we apply SAMD to two physiological signals, impedance pneumography and electroencephalography. Comparison with existing solutions, including linear regression, recursive diffeomorphism-based regression and multiresolution mode decomposition, shows that our proposal can provide an accurate and meaningful decomposition with computational efficiency.

Objective: Our goal is to use existing and to propose new time-frequency entropy measures that objectively evaluate the improvement on epileptic patients after medication by studying their resting state EEG recordings. An increase in the complexity of the signals would confirm an improvement in the general state of the patient. Methods: We review the Rényi entropy based on time-frequency representations, along with its time-varying version. We also discuss the entropy based on singular value decomposition computed from a time-frequency representation, and introduce its corresponding time-dependant version. We test these quantities on synthetic data. Friedman tests are used to confirm the differences between signals (before and after proper medication). Principal component analysis is used for dimensional reduction prior to a simple threshold discrimination. Results: Experimental results show a consistent increase in complexity measures in the different regions of the brain. These findings suggest that extracted features can be used to monitor treatment. When combined, they are useful for classification purposes, with areas under ROC curves higher than 0.93 in some regions. Conclusion: Here we applied time-frequency complexity measures to resting state EEG signals from epileptic patients for the first time. We also introduced a new time-varying complexity measure. We showed that these features are able to evaluate the treatment of the patient, and to perform classification. Significance: The time-frequency complexities, and their time-varying versions, can be used to monitor the treatment of epileptic patients. They could be applied to a wider range of problems.

The modulus of time-frequency representations, like the short-time Fourier or wavelet transforms, of a multicomponent signal exhibit ridges from which one usually computes estimations of the instantaneous frequencies of the modes making up the signal. But, due to the finite frequency resolution, the estimations thus obtained are piecewise constant. Our aim in this letter is to introduce a novel method for the estimation of the instantaneous frequencies of the modes based on the modeling of the modulus of the short-time Fourier transform, and then to propose a novel technique for mode retrieval. Numerical experiments carried out on both simulated and real signals demonstrate the benefits of the proposed approach over others based on the short-time Fourier transform.

This paper addresses the problem of estimating the instantaneous frequency (IF) and amplitude of the modes composing a non-stationary multi-component signal in the presence of noise. A novel observation model for the signal spectrogram is developed within a Bayesian framework to handle intricate configurations involving noise or overlapping components. The model parameters are estimated using a stochastic variant of the Expectation-Maximization algorithm, bypassing the computationally expensive joint parameter estimation from the posterior distribution. We then design an algorithm for instantaneous amplitude and frequency estimation that accounts for overlap and amplitude variations of the components. To assess the performance of the proposed method, we conduct experiments on both real-world and simulated signals, involving separated or crossing modes. The benefits of our method in terms of efficiency compared with several state-of-the art techniques appear to be significant in that latter case, but also when the amplitude of the components are varying across time.

In this paper, we define a new ridge detector that enables to localize strong interference in multicomponent signals in the time-frequency (TF) plane. Each mode of a multicomponent signal can usually be associated with a ridge in the TF plane, but this is no longer the case when strong interferences occur in the signal. The new ridge detector we propose is thus designed to determine when such situations happen in the TF plane. We show that this knowledge helps to determine an appropriate window length in the definition of the spectrogram, as well as the nature of the strong interference detected. An application of the proposed approach to voice signals concludes the paper.