Cyclostationarity (CS) has proven to be effective in the treatment and identification of signal components for diagnostic and prognosis purposes. CS research has focused on algorithms, in terms of simplicity and computational efficiency. The performance of algorithms largely depends on the signals being analyzed. The objective of this research paper is to exploit the CS characteristics of signals in the context of morphological component analysis (MCA) method. It proposes a novel methodology used for separating between the periodic (First-Order Cyclostationarity: CS1) and random (Second-Order Cyclostationarity: CS2) sources by means of one sensor measurement. This MCACS2 methodology is based on MCA, where each of the two sources is sparsely represented by a special dictionary: i) the CS1 periodic structure is sparsely represented by means of the Discrete Cosine Transform dictionary, and ii) the CS2 random component is sparsely represented by a new proposed dictionary derived from Envelope Spectrum Analysis. Subsequently, a simulation study is performed in order to validate the proposed new MCACS2 method followed by tests on real GRF biomechanical signals. The result concludes by stating that such a novel algorithm provides an additional way for the exploitation of cyclostationarity and may be useful in other domain applications. (C) 2016 Elsevier Inc. All rights reserved.

It was discovered that the original online version of the above article contained an incorrect affiliation for Dr. Anna Ewa Dudek that was not the fault of the author. The Publisher has resupplied (reposted and replaced) the XML and online PDF of the article. Unfortunately, the discovery of the error was at a point too late to correct the printed issue. Elsevier regrets and apologizes for any inconvenience caused by posting a new version of this article online, but hopes that the reader will understand the reasons for doing so.

Dans le cadre de l’analyse de signaux mécaniques ou biomécaniques les outils d’aide à la décision reposent sur des hypothèses statistiques fortes: loi de probabilité normale, stationnarité des variables, variables centrées, variables indépendantes,…Or ces hypothèses sont parfois non vérifiées et engendrent des décisions erronées. Ce travail a pour objectif de proposer des méthodes qui font abstractions de certaines hypothèses et notamment de la stationnarité et de la gaussiannité des variables aléatoires. Dans cette thèse, nous avons revisité certaines méthodes de ré échantillonnages statistiques et de bootstrap et développé d’autres en incluant la cyclostationnarité des signaux. Ensuite, nous avons appliqué ces méthodes pour l’analyse de signaux biomécaniques provenant de coureurs expérimentés et d’une population de personnes âgées. Les résultats obtenus ont permis de mettre en évidence des changements significatifs dans le contenu fréquentiel du second ordre des signaux étudiés. Ces changements ont été des indicateurs très pertinents pour la description et la caractérisation de la fatigue d’un coureur professionnel, d’une part, et pour la compréhension du mécanisme complexe de la marche à pied simple et avec tâche cognitive chez les personnes âgées d’autre part

In this paper we propose a new technique of significant frequencies detection for periodically correlated time series. New method is based on bootstrap technique called Generalized Seasonal Block Bootstrap. Bootstrap procedure is applied in the time domain and then Fourier representation of autocovariance function for bootstrap samples is used. Finally, the simultaneous confidence intervals for the absolute values of the Fourier coefficients are calculated. The results are compared in the small simulation study with similar tools based on subsampling methodology and moving block bootstrap for almost periodic processes.

Cyclostationarity (CS), as characteristic of signals, is a technique that offers diagnostic advantages for the analysis of failures, faults and disturbances which are related to a system being examined. The aim of this paper is to introduce the concept of CS for signals and to present possibilities of statistical resampling procedures for the estimation of second order statistics of such signals. The resampling methods treated in this paper are referred to as subsampling and moving block bootstrap (MBB). A description of these methods is presented and their applicability to CS simulated data is proved. The comparison between those two procedures shows that subsampling seems to be more efficient and more relevant than MBB. The subsampling-based CS analysis of biomechanical ground reaction force signals (GRF signals), coming from a high level professional runner, proves the second order cyclostationary (CS2) nature of the GRF signals. Moreover, it enables us to distinguish successfully the CS2 cyclic frequencies of the signals under consideration. Some new indicators based on the subsampling procedure are also proposed. This allows a better characterization and a full innovative description of the different fatigue states of a runner.

In this paper the Generalized Seasonal Block Bootstrap (GSBB) method is applied to the first and the second order characteristics of the cyclostationary (CS) signal. The new method for detection of the significant frequencies in the Fourier expansions of the mean and the autocovariance functions of CS processes is provided. The consistency of GSBB is shown. Finally, the bootstrap pointwise and simultaneous confidence intervals are constructed and hence hypothesis tests for the presence of the first and the second order cyclostationarity can be performed. The real data example is presented to show the possible applications of our results. Moreover, the simulation study was performed to check the efficiency and robustness to the noise of the considered method.

The objective of the research is to develop new methods or indicators regarding cyclostationarity (CS) that could clearly point out and differentiate between walking disorder signals. Normal human locomotion is the rather grand term given to the description of walking by individuals who fall within the range considered as “normal”, and is seen as a sequence of cyclic and repeated gestures. It is a highly individual and variable activity influenced by many various factors. Analysis and treatment of such sequences, are demonstrated, and have proved that such processes are cyclostationary. This article suggests that “Kurtosis” provides a strong indicator of CS, and shows empirically the existence of a relationship between the “Kurtosis” and the known indicator of CS; specifically “the degree of cyclostationarity (DCS)”. An empirical study on the biomechanics of locomotion is performed with the objective of using it as supportive evidence of that relationship.

Cyclostationarity (CS) is relatively a new technique that offers diagnostic advantages for analysis of faults related to a studied system. The aim of this paper is to address the issue of separating the second-order cyclostationary (CS2) component from the first-order cyclostationary component (CS1) of a signal when low speed fluctuations exist. A bootstrap-based method called Generalized Seasonal Block Bootstrap (GSBB) is applied on walking signals coming from elderly in order to characterize walking in this population and possible age-related walking disturbance, in one hand, and to explore and analyze the influence of low speed fluctuations on the first and second orders cyclostationary properties of signals, on the other hand. Two GSBB-based indicators have also been proposed to characterize the quality of the CS1 and CS2 estimates.

In last decades, a well-studied characteristic of signals called Cyclostationarity (CS) has provided very important survey, highlighting the impact of CS models on signal analysis in telecommunication, mechanical, acoustic, biomechanical and econometric signals. It is a technique that offers diagnostic advantages for the analysis of failures, faults and disturbances which are related to a system being examined. The aim of this paper is to introduce the concept of CS for signals and to present possibilities of statistical resampling procedures available for such signals. The resampling method treated in this paper is referred to as Subsampling. A description of this method is presented and its applicability to CS simulated and real data is proved. This implies, in particular, that statistical CS analysis can be carried out without the assumption of Gaussianity on the CS process under consideration.