The localization of interference associated with crossing modes in thetime-frequency(TF) plane is of significant interest when the objective is to separate these modes. Prior to localizing mode crossings, it is essential to determine whether the observed interference arises from closely spaced modes or from actual mode crossings. In this paper, we propose a novel technique to discriminate between these different types of interference in the TF plane and to subsequently localize mode crossings. The proposed approach exhibits strong adaptability across a wide range of scenarios and demonstrates robustness to noise, as confirmed by simulation results.

This paper aims at building a new instantaneous frequency (IF) estimator of the modes making up non-stationary multi-component signals, using reassignment operators used in Fourier-based synchrosqueezing transforms (FSSTs) and linear chirp points detection. Reassignment operators provide with different IF estimates, depending on the assumption made on the local polynomial order of the phase of the studied mode. In practice, it is difficult to estimate locally which order fits the best, and to choose too high an order, typically larger than two, when not necessary results in both an inaccurate estimation and an increased sensitivity to noise. To circumvent this, we propose to localize linear chirp points in modes to find out where second order phase approximation is sufficient for the estimation, and then build a new IF estimate based on a weighted spline approximation based on these points. Numerical results show the improvement brought by the proposed approach in noisy situations over classical IF estimators used in FSSTs.

In this work, we explore the problem of making synchrosqueezing transform adaptive. To deal with multicomponent signals, existing methods use a fixed order N, thus assuming all the modes making up the signal have order N polynomial phases. To go beyond this limitation, we introduce a new criterion based on the concentration of the representation to locally choose the best order for the synchrosqueezing transform. We study the performance of the proposed approach in terms of the error with respect to the ideal time-frequency representation, both on synthetic and real signals.

In this paper, we propose a novel approach to classify the spectrogram zeros (SZs) of multicomponent signals based on the analysis of the Voronoï cells associated with these zeros. More precisely, the characterization of the distribution of the spectrogram maxima of a complex white Gaussian noise along the edges of the Voronoï cells associated with SZs enables us to derive an algorithm to classify the different types of zeros present in the spectrogram of a multicomponent signal. Numerical applications on simulated signals confirm the relevance of the proposed classification algorithm, and an illustration on a real signal concludes the paper.

Voice health is traditionally assessed by methods that rely on the perception of a clinician, who integrates auditory and visual cues in order to reach a conclusion about the voice under evaluation. However, these tasks suffer from inter-professional variability due to its subjective nature, which is why more objective, computational-based methods are of interest. Two examples of such subjective tasks are the classification of voices in three types according to their periodicity, also termed voice typing, and the evaluation of six aspects of voice quality by means of the consensus auditory-perceptual evaluation of voice (CAPE-V) protocol. In this paper, two approaches to emulate each of those tasks are introduced, based on simple features extracted from the second-order scattering transform coefficients and support vector machines. Firstly, a system for automatic voice typing was trained and its classification performance was evaluated for intra and inter-dataset trials using two widely known corpora. Accuracies above 80%, comparable to the state-of-the-art, were found for all the experiments conducted. Secondly, a multidimensional, multioutput regression chain model was used to automatically grade the voice quality features of the CAPE-V protocol, obtaining errors and correlation coefficients that are comparable to those found for three human raters.

Voice jitter is defined as a random perturbation of the glottal cycle duration which can be useful for voice parametrization and that usually depends on finding fiducial points in this signal. In this paper, a novel application of the Fourier-based high-order synchrosqueezing (FSSTN) operators on voice signals is introduced for voice jitter estimation without period-segmentation. To this end, an innovative interpretation of the relative jitter formula in terms of the total variation of the sequence of periods is proposed. This allows us to derive an algorithm for jitter estimation that uses the (continuous) instantaneous fundamental frequency of the signal and its first derivative (chirp rate) which can be obtained, respectively, from the local complex frequency and the local complex modulation FSSTN operators. Numerical experiments using synthetic signals with known true jitter show that this novel approach yields similar results to other state-of-the-art method, PRAAT, for true jitter within the range [0.2%, 1.2%], and that it outperforms PRAAT for true jitter values in the range [1%, 15%]. The here proposed method seems a promising tool for voice jitter estimation and constitutes a novel application of the high-order synchrosqueezing operators for voice signals with potential impact on jitter modeling and on the clinical field.

In this paper, we investigate the determination of an optimal window length associated with the computation of the short time Fourier transform of multicomponent signals. In recent years the Rényi entropy has been widely used for that purpose, but the understanding of the significance of the obtained minimum in relation with the studied signal is still partial. In this paper, we explain in what way the window minimizing the Rényi entropy reflects the modulation of the modes making up the signal, and in which circumstances to use such a window is actually relevant.

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.

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.

We propose new multichannel time-frequency complexity measures to evaluate differences on magnetoencephalograpy (MEG) recordings between healthy young and old subjects at rest at different spatial scales. After reviewing the Rényi and singular value decomposition entropies based on time-frequency representations, we introduce multichannel generalizations, using multilinear singular value decomposition for one of them. We test these quantities on synthetic data, illustrating how the introduced complexity measures focus on number of components, nonstationarity, and similarity across channels. Friedman tests are used to confirm the differences between young and old groups, and heterogeneity within groups. Experimental results show a consistent increase in complexity measures for the old group. When analyzing the topographical distribution of complexity values, we found clusters in the frontal sensors. The complexity measures here introduced seem to be a better indicator of the neurophysiologic changes of aging than power envelope connectivity. Here, we applied new multichannel time-frequency complexity measures to resting-state MEG recordings from healthy young and old subjects. We showed that these features are able to reveal regional clusters. The multichannel time-frequency complexities can be used to monitor the aging of subjects. They also allow a mutual information approach, and could be applied to a wider range of problems.

This paper introduces a 2D extension of the empirical mode decomposition (EMD), through a novel approach based on unconstrained optimization. EMD is a fully data-driven method that locally separates, in a completely data-driven and unsupervised manner, signals into fast and slow oscillations. The present proposal implements the method in a very simple and fast way, and it is compared with the state-of-the-art methods evidencing the advantages of being computationally efficient, orientation-independent, and leads to better performances for the decomposition of amplitude modulated-frequency modulated (AM-FM) images. The resulting genuine 2D method is successfully tested on artificial AM-FM images and its capabilities are illustrated on a biomedical example. The proposed framework leaves room for an nD extension (n > 2 ).

In this paper an algorithm based on the ensemble empirical mode decomposition (EEMD) is presented. The key idea on the EEMD relies on averaging the modes obtained by EMD applied to several realizations of Gaussian white noise added to the original signal. The resulting decomposition solves the EMD mode mixing problem, however it introduces new ones. In the method here proposed, a particular noise is added at each stage of the decomposition and a unique residue is computed to obtain each mode. The resulting decomposition is complete, with a numerically negligible error. Two examples are presented: a discrete Dirac delta function and an electrocardiogram signal. The results show that, compared with EEMD, the new method here presented also provides a better spectral separation of the modes and a lesser number of sifting iterations is needed, reducing the computational cost.