The Power Law Applied to the Windowed Fourier Transform

The windowed Fourier transform is one of the most widely used time-frequency representations. In order to use this technique several parameters must be defined according to the signal analyzed. In this paper are studied the effects of the type, the shape, the length and the overlap of the windows. A power law/fractional window that we call fractional is defined and a new method for tuning the window parameters is presented. The study is based on the information theory and is applied to signals captured during the movement of a robotic manipulator. The experimental results demonstrate the applicability and the effectiveness of the proposed approach.N/

Linear and synchrosqueezed time–frequency representations revisited:overview, standards of use, resolution, reconstruction, concentration, and algorithms

Time–frequency representations (TFRs) of signals, such as the windowed Fourier transform (WFT), wavelet transform (WT) and their synchrosqueezed versions (SWFT, SWT), provide powerful analysis tools. Here we present a thorough review of these TFRs, summarizing all practically relevant aspects of their use, reconsidering some conventions and introducing new concepts and procedures to advance their applicability and value. Furthermore, a detailed numerical and theoretical study of three specific questions is provided, relevant to the application of these methods, namely: the effects of the window/wavelet parameters on the resultant TFR; the relative performance of different approaches for estimating parameters of the components present in the signal from its TFR; and the advantages/drawbacks of synchrosqueezing. In particular, we show that the higher concentration of the synchrosqueezed transforms does not seem to imply better resolution properties, so that the SWFT and SWT do not appear to provide any significant advantages over the original WFT and WT apart from a more visually appealing pictures. The algorithms and Matlab codes used in this work, e.g. those for calculating (S)WFT and (S)WT, are freely available for download

Generalized instantaneous parameters and window matching in the time-frequency plane

In this paper, the concept of instantaneous parameters, which has previously been associated exclusively with 1-D measures like the instantaneous frequency and the group delay, are extended to the 2-D time-frequency plane, Such generalized instantaneous parameters are associated with the short-time Fourier transform, They may also be interpreted as local moments of certain time-frequency distributions, It is shown that these measures enable local signal behavior to be characterized in the time-frequency plane for nonstationary deterministic signals, The usefulness of the generalized instantaneous parameters is demonstrated in their application to optimal selection of windows for spectrograms. This is achieved through window matching in the time-frequency plane, An algorithm is provided that illustrates the performance of this window matching, Results based on simulated and real data are presented

Réflectométrie appliquée à la détection de défauts non francs dans les torons de câbles

Ces travaux de thèse portent sur la détection de défauts non francs dans des structures filaires particulières : les lignes de transmission a multiconducteurs (MTL), aussi appelées torons de câbles. Couramment employées pour le diagnostic de réseaux filaires, les méthodes par réflectométrie ne sont, pour l'heure, pas suffisamment performantes pour détecter de tels défauts. Par ailleurs, elles n'ont, en général, été étudiées et développées que pour des lignes simples, ou les phénomènes de couplages électromagnétiques entre les conducteurs (diaphonie) ne sont pas présents. Ces derniers sont cependant porteurs d'information supplémentaire sur l'état du câble. Les utiliser permettrait d'accroître la sensibilité de détection aux défauts. L'objectif est de proposer une nouvelle méthode de réflectométrie, tirant profit des signaux de diaphonie pour détecter les défauts non francs. Une telle méthode présente également l'avantage d'être adaptée aux structures en toron. Après avoir étudié l'impact d'un défaut non franc sur les paramètres caractéristiques d'une MTL et sur les signaux de diaphonie, une méthode, la "Cluster Time Frequency Domain Reflectometry ", a pu être proposée. Il s'agit d'un procédé en trois étapes. Des mesures par réflectométrie temporelle sont tout d'abord réalisées à l'entrée de la ligne à diagnostiquer. Tous les signaux présents, y compris ceux de diaphonie, sont enregistrés. Un traitement temps-fréquence leur est ensuite appliqué afin d'amplifier la présence d'éventuels défauts. Enfin, un algorithme de clustering, spécifiquement développé pour le diagnostic filaire, est utilisé de manière a bénéficier de l'ensemble de l'information disponibleResearch works presented in this thesis rely on detecting soft faults (incipient faults) in specic wiring structures : multiconductor transmission lines (MTL), also known as bundles of wires. Reflectometry methods, often used for the diagnosis of wiring networks, aren't for now efficient enough at detecting such defects. Besides, they have been designed for single lines only, where electromagnetic coupling between conductors (crosstalk) is not to be considered. However such phenomenon can provide more information about the state of the cable. Using this information could enable us to detect soft faults more easily. Our goal is to propose a new reflectometry method, which takes advantage of crosstalk signals in order to detect incipient faults. Such a tool has also the advantage of being well-adapted to bundles of cables. Thanks to the preliminary study of the impact of soft faults on the characteristic parameters of a MTL and on crosstalk signals, a method called "Cluster Time Frequency Domain Reflectometry ", has been proposed. It is a three step process. Firts temporal reflectometry measurements are made at the beginning of the line under test. All the available signals, even crosstalk ones, are recorded. A time-frequency process is then applied on them, in order to amplify the presence of defects. Finally, a clustering algorithm, that has been specically developed for wiring diagnosis, is used to benefit from the whole available informationPARIS-EST-Université (770839901) / SudocSudocFranceF