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Many people experience mild stress in modern society which raises the need for an improved understanding of psychophysiological responses to stressors. Heart rate variability (HRV) may be associated with a flexible network of intricate neural structures which are dynamically organized to cope with diverse challenges. HRV was obtained in thirty-three healthy participants performing a cognitive task both with and without added stressors. Markers of neural autonomic control and neurovisceral complexity (entropy) were computed from HRV time series. Based on individual anxiety responses to the experimental stressors, two subgroups were identified: anxiety responders and non-responders. While both vagal and entropy markers rose during the cognitive task alone in both subgroups, only entropy decreased when stressors were added and exclusively in anxiety responders. We conclude that entropy may be a promising marker of cognitive tasks and acute mild stress. It brings out a new central question: why is entropy the only marker affected by mild stress? Based on the neurovisceral integration model, we hypothesized that neurophysiological complexity may be altered by mild stress, which is reflected in entropy of the cardiac output signal. The putative role of the amygdala during mild stress, in modulating the complexity of a coordinated neural network linking brain to heart, is discussed.

Proposed early in the 90ies, the detrended fluctuation analysis (DFA) can be used to estimate the Hurst exponent and has been proven relevant in various applications, from economics to biomedical. For the last years, variants have been proposed. They differ in the way to estimate the trend of the centered integrated signal. In this paper, we recall the main principles of some of these methods, provide explanations on the behaviours of the algorithms and analyze the relevance of new variants based on the Savitzky-Golay filter, also known as the LOESS approach, and the LOWESS. They bridge the gap between the DFA and the detrending moving average (DMA). We hence show that the LOESS-based method is a generalization of the DMA.

A great deal of interest has been paid to enhance the radar range resolution for the last decades. One of the techniques is to construct a waveform combining inter-pulse and intra-pulse modulations. In this paper, stepped frequency (SF) waveform is used to represent the former, whereas phase coding (PC) is considered for the latter. To obtain the high-resolution range profile (HRRP) of a target induced by an SF waveform at the receiver, one of the approaches is the frequency domain (FD) algorithm. It has been successfully applied with SF linear frequency modulation waveforms. However, based on our investigations, processing the SFPC waveform with the FD algorithm does not lead to the performance, in terms of peak sidelobe ratio (PSLR) and integrated sidelobe ratio (ISLR), of the single-carrier phase coding (SCPC) waveform processed with a matched filter (MF). To overcome these drawbacks, we propose to split the spectrum of a phase coded pulse into a predetermined number of portions, and then to successively transmit the time-domain transformed versions of these various portions. The received echoes are then processed with a modified version of the FD algorithm. Our analysis and simulations show that the proposed waveform can be characterized by a PSLR and an ISLR close to those of the SCPC processed with MF in some scenarios.

In signal processing, ARMA processes are widely used to model short-memory processes. In various applications, comparing or classifying ARMA processes is required. In this paper, our purpose is to provide analytical expressions of the divergence rates of the Kullback-Leibler divergence, the Renyi divergence (RD) of order α and their symmetric versions for two Gaussian ARMA processes, by taking advantage of results such as the Yule-Walker equations and notions such as inverse filtering. The divergence rates can be interpreted as the sum of different quantities: power of one ARMA process filtered by the inverse filter associated with the second ARMA process, cepstrum, etc. Finally, illustrations show that the ranges of values taken by the divergence rates of the RD are sensitive to α, especially when the latter is close to 1.

International audience; The detrended fluctuation analysis (DFA) and its higher-order variant make it possible to estimate the Hurst exponent and therefore to quantify the long-range dependence of a random process. These methods are popular and used in a wide range of applications where they have been proven to be discriminative to characterize or classify processes. Nevertheless, in practice, the signal may be short-memory. In addition, depending on the number of samples available, there is no guarantee that these methods provide the true value of the Hurst exponent, leading the user to draw erroneous conclusions on the long-range dependence of the signal under study. In this paper, using a matrix formulation and making no approximation, we first propose to analyze how the DFA and its higher-order variant behave with respect to the number of samples available. Illustrations dealing with short-memory data that can be modeled by a white noise, a moving-average process and a random process whose autocorrelation function exponentially decays are given. Finally, to avoid any wrong conclusions, we propose to derive abacuses linking the value provided by the DFA or its variant with the properties of the signal and the number of samples available.

International audience; To estimate the Hurst exponent of a mono-fractal process, the detrended fluctuation analysis (DFA) is based on the estimation of the trend of the integrated process. The latter is subtracted from the integrated process. The power of the residual is then computed and corresponds to the square of the fluctuation function. Its logarithm is proportional to the Hurst exponent. In the last few years, a few variants of this method have been proposed and differ in the way of estimating the trend. Our contribution in this paper is threefold. First, we introduce a new variant of the DFA, based on a regularized least-square criterion to estimate the trend. Then, the influence of the regularization parameter on the fluctuation function is analyzed in two cases: when the process is wide sense stationary and when it is not. Finally, an application is presented in the field of aeronautics to characterize an attentional impairment: the visual tunneling.

International audience; Target classification can be of real interest for sea surveillance in both civil and military contexts. To address this issue, we present two approaches based on the Singer model. The latter has the advantage of covering a wide range of motions depending on the values of its parameters. Given noisy observations, the first method aims at estimating the motion model parameters by taking advantage of the properties of the correlation function of the estimated acceleration. It is based on a genetic algorithm. The second approach is on-line and consists in deriving a joint tracking and classification (JTC) method. Based on various simulations, we study their respective relevance in different operational settings. The proposed JTC corresponds to the best compromise in terms of performance and number of samples required.

International audience; The non-linear frequency modulation (NLFM) waveform is one of the existing waveforms that can be used in high range resolution radar applications. However, a high sampling frequency and consequently an expensive ADC are required. To overcome this drawback while taking advantage of the features of the NLFM waveform, we suggest approximating the wideband NLFM waveform by a piecewise linear waveform and using it in a stepped frequency (SF) framework. Thus, a variable chirp rate SF-LFM waveform is proposed where SF is combined with a train of LFM pulses having different chirp rates, durations, and bandwidths. In this paper, these parameters are derived from a tangent-based NLFM waveform. At the receiver, a generalized version of the time domain (TD) algorithm is proposed to process the received echoes. Our purpose is to obtain the high range resolution profile (HRRP) whose properties are of the same magnitude orders as those obtained using a tangent-based NLFM waveform. These properties are the peak sidelobe ratio, the integrated sidelobe, and the range resolution. Toward this goal, a multi-objective optimization issue is addressed to deduce the parameters of the proposed waveform by using two types of approaches based on evolutionary algorithms. Their relevance is compared. Our analysis and simulations show that the proposed approaches attain the targeted performance goals with a smaller sampling frequency at the receiver.

International audience; The detrended fluctuation analysis (DFA) and its variants such as the detrended moving average (DMA) are widely used to estimate the Hurst exponent. These methods are very popular as they do not require advanced skills in the field of signal processing and statistics while providing accurate results. As a consequence, a great deal of interest has been paid to compare them and to better understand their behaviors from a mathematical point of view. In this paper, our contribution is threefold. Firstly, we propose another variant avoiding the discontinuities between consecutive local trends of the DFA by a priori constraining them to be continuous. Secondly, we show that, in all these approaches, the square of the fluctuation function can be presented in a similar matrix form. When the process is wide-sense stationary (w.s.s.), the latter can be seen as the power of the output of a linear filtering whose frequency response depends on the given method. In the general case, an interpretation of the square of the fluctuation function is also given by expressing it as the convolution between the 2D-Fourier transform of two matrices, one whose elements correspond to the instantaneous correlation function of the signal and the other which depends on the detrending method. To end up, an illustration is provided in the field of avionics for the detection of the visual tunneling, a deleterious cognitive state.

The symmetric Kullback–Leibler divergence known as Jeffrey's divergence (JD) has found applications in signal and image processing, from radar clutter modeling to texture analysis. Recently, several studies were done on the JD between ergodic wide-sense stationary autoregressive (AR) and/or moving average (MA) processes. It was shown that the so-called asymptotic JD increment can be useful to compare ergodic wide-sense stationary ARMA processes. An interpretation of the asymptotic JD increment was also proposed. It consists in calculating the power of the first process filtered by the inverse filter associated with the second process, and conversely. However, in some biomedical applications, econometrics and other areas, long-memory processes have rather to be studied. Therefore, this paper aims at addressing the JD between ergodic wide-sense stationary autoregressive fractionally integrated moving average (ARFIMA) processes. More particularly, we study the influence of the ARFIMA parameters on the value of the asymptotic JD increment. Then, we analyze if the interpretation of the asymptotic JD increment based on inverse filtering is still valid for this type of process. Finally, some simulation results illustrate the theoretical analysis.

In signal and image processing, Jeffrey's divergence (JD) is used in many applications for classification, change detection, etc. The previous studies done on the JD between ergodic wide-sense stationary (WSS) autoregressive (AR) and/or moving average (MA) processes state that the asymptotic JD increment, which is the difference between two JDs based on k and ( k − 1 ) -dimensional random vectors when k becomes high, tends to a constant value, except JDs which involve a 1st-order MA process whose power spectral density (PSD) is null for one frequency. In this paper, our contribution is threefold. We first propose an interpretation of the asymptotic JD increment for ergodic WSS ARMA processes: it consists in calculating the power of the first process filtered by the inverse filter associated with the second process and conversely. This explains the atypical cases identified in previous works and generalizes them to any ergodic WSS ARMA process of any order whose PSD is null for one or more frequencies. Then, we suggest comparing other random processes such as noisy sums of complex exponentials (NSCE) by using the JD. In this case, the asymptotic JD increment and the convergence speed towards the asymptotic JD are useful to compare the processes. Finally, NSCE and pth-order AR processes are compared. The parameters of the processes, especially the powers of the processes, have a strong influence on the asymptotic JD increment.

This paper proposes a new method for identifying ARMA models in the presence of additive white noise. The method operates with two main steps. First, the noisy ARMA model is approximated by the sum of an high-order AR model with an additive white noise. The parameters of the high-order AR model as well as the driving noise and the additive noise variances are estimated by using an errors-in-variables approach. Second, the coefficients of the ARMA model are extracted from those of the AR model previously identified by means of existing techniques. In particular, three different methods are considered and compared for solving the second step. The effectiveness of the described identification procedure has been tested by Monte Carlo simulations and compared with a prediction error method.

Even if they can be outperformed by other methods, the detrended fluctuation analysis (DFA) and the detrended moving average (DMA) are widely used to estimate the Hurst exponent because they are based on basic notions of signal processing. For the last years, a great deal of interest has been paid to compare them and to better understand their behaviors from a mathematical point of view. In this paper, our contribution is the following: we first propose to express the square of the so-called fluctuation function as a 2D Fourier transform (2D-FT) of the product of two matrices. The first one is defined from the instantaneous correlations of the signal while the second, called the weighting matrix, is representative of each method. Therefore, the 2D-FT of the weighting matrix is analyzed in each case. In this study, differences between the DFA and the DMA are pointed out when the approaches are applied on non-stationary processes.

The detrended fluctuation analysis (DFA) is widely used to estimate the Hurst exponent. Although it can be outperformed by wavelet based approaches, it remains popular because it does not require a strong expertise in signal processing. Recently, some studies were dedicated to its theoretical analysis and its limits. More particularly, some authors focused on the so-called fluctuation function by searching a relation with an estimation of the normalized covariance function under some assumptions. This paper is complementary to these works. We first show that the square of the fluctuation function can be expressed in a similar matrix form for the DFA and the variant we propose, called Continuous-DFA (CDFA), where the global trend is constrained to be continuous. Then, using the above representation for wide-sense-stationary processes, the statistical mean of the square of the fluctuation function can be expressed from the correlation function of the signal and consequently from its power spectral density, without any approximation. The differences between both methods can be highlighted. It also confirms that they can be seen as ad hocwavelet based techniques.

Because most humans live and work in populated environments, researchers recently took into account that people may not only experience first-hand stress, but also second-hand stress related to the ability to empathically share another person’s stress response. Recently, researchers have begun to more closely examine the existence of such empathic stress and highlighted the human propensity to physiologically resonate with the stress responses of others. As in case of first-hand stress, empathic stress could be deleterious for health if people experience exacerbated activation of hypothalamic–pituitary–adrenal and autonomic nervous systems. Thus, exploring empathic stress in an observer watching someone else experiencing stress is critical to gain a better understanding of physiological resonance and conduct strategies for health prevention. In the current study, we investigated the influence of empathic stress responses on heart rate variability (HRV) with a specific focus on nonlinear dynamics. Classic and nonlinear markers of HRV time series were computed in both targets and observers during a modified Trier social stress test (TSST). We capitalized on multiscale entropy, a reliable marker of complexity for depicting neurovisceral interactions (brain-to-heart and heart-to-brain) and their role in physiological resonance. State anxiety and affect were evaluated as well. While classic markers of HRV were not impacted by empathic stress, we showed that the complexity marker reflected the existence of empathic stress in observers. More specifically, a linear model highlighted a physiological resonance phenomenon. We conclude on the relevance of entropy in HRV dynamics, as a marker of complexity in neurovisceral interactions reflecting physiological resonance in empathic stress.

Micro-Doppler induced by mechanical vibrating or rotating structures in a radar target is possibly useful for its detection, classification and recognition. In a previous work, pseudo-Zernike moments (PZMs) were used as micro-Doppler features for classification. Despite of their promising classification rates, the choice of PZMs is debatable because other types of moments exist. In this paper, our purpose is to compare various kinds of micro-Doppler features such as Zernike moments, PZMs, orthogonal Mellin-Fourier moments, Legendre moments and Krawtchouk moments in order to evaluate which moments are the most relevant in terms of reconstruction ability, computational cost and micro-Doppler classification rate. Advantages and drawbacks of each family of moments are also given. Through the simulations we carried out, when the signal is disturbed by an additive white noise and the signal-to-noise ratio is low, the use of Krawtchouk moments as micro-Doppler features turns out to be the best compromise.

Like other divergences, Jeffrey's divergence (JD) is used for change detection, for model comparison, etc. Recently, a great deal of interest has been paid to this symmetric version of the Kullback-Leibler (KL) divergence. This led to analytical expressions of the JD between autoregressive (AR) processes, moving-average (MA) processes, either noise-free or disturbed by additive white noises, as well as ARMA processes. In this paper, we propose to study the JD between processes that are defined as sums of complex-valued sinusoidal processes disturbed by additive white noises. We show that the JD tends to a stationary behavior when the number of variates becomes large. The derivative of the JD becomes a constant that depends on the parameters defining the processes. The convergence speed towards this stationary regime depends on the differences between the normalized angular frequencies. The smaller the difference, the slower the convergence. This result can be obtained by interpreting some steps to compute the JD as orthogonal projections. Some examples illustrate the theoretical analysis.

Various works have been carried out about the Jeffrey's divergence (JD) which is the symmetric version of the Kullback-Leibler (KL) divergence. An expression of the JD for Gaussian processes can be deduced from the definition of the KL divergence and the expression of the Gaussian-multivariate distributions of k-dimensional random vectors. It depends on the k × k Toeplitz covariance matrices of the stationary processes. However, the resulting computational cost may be high as these matrices must be inverted and it is all the higher as k increases. To circumvent this problem, a recursive expression can be obtained for real 1st-order autoregressive (AR) processes. When they are disturbed by additive uncorrelated white noises, we showed that when k becomes large, the derivative of the JD with respect to k tends to be constant. This constant is sufficient to compare the noisy AR processes. In this paper, we propose to extend our work to AR moving-average (MA) processes with one AR term and one MA term. Some examples illustrate the theoretical analysis.

This study deals with an interweave cognitive-radio (CR) system, where an uplink orthogonal frequency-division multiple access system is considered for the primary users (PUs). Our purpose is to estimate the PU carrier frequency offsets (PU-CFOs) as well as the channels to estimate the transmitted symbols. However, in wideband wireless communications, the PU received-signal spectrum usually exhibits a localised fading because of the multipath propagation channel. When the PU faded frequencies are used by the CR system, the PU system is contaminated by a CR narrowband interference (CR-NBI). In that case, if a Kalman filter (KF)-based approach is used for the estimations of the CFOs and the channels, the state-space representation does not necessarily take into account the CR-NBI; this hence has a negative impact on the algorithm performance. Therefore the authors propose to make this solution more robust to the CR-NBI by detecting when it appears and disappears to avoid using the data disturbed by the CR-NBI. The authors’ contribution is to assume that the CR-NBI is because of the transmission of contiguous blocks and to propose various criteria based on the covariance matrix of the KF innovation.

International audience; For a battery driven terminal, the power amplifier (PA) efficiency must be optimized. Consequently, non-linearitiesmay appear at the PA output in the transmission chain. To compensate these distortions, one solution consists of using a digital detector based on a Volterra model of both the PA and the channel and a Kalman filter (KF) based algorithm to jointly estimate the Volterra kernels and the transmitted symbols. Here, we suggest addressing this issue when dealing with cognitive radio (CR). In this case, additional constraints must be taken into account. Since the CR terminal may switch from one sub-band to another, the PA non-linearities may vary over time. Therefore, we propose to design a digital detector based on an interacting multiple model combining various KF based estimators using different model parameter dynamics. This makes it possible to track the time variations of the Volterra kernels while keeping accurate estimateswhen those parameters are static. Furthermore, the single and multicarrier cases are addressed and validated by simulationresults. Our solution corresponds to a compromise between computational cost and bit-error-rate performance.

This paper deals with the analysis of the Jeffrey's divergence (JD) between an autoregressive process (AR) and a sum of complex exponentials (SCE), whose magnitudes are Gaussian random values, which is then disturbed by an additive white noise. As interpreting the value of the JD may not be necessarily an easy task, we propose to give an expression of the JD and to analyze the influence of each process parameter on it. More particularly, we show that the ratios between the variance of the additive white noise and the variance of the AR-process driving process on the one hand, and the sum of the ratios between the SCE process power and the AR-process PSD at the normalized angular frequencies on the other hand, has a strong impact on the JD. The 2-norm of the AR-parameter has also an influence. Illustrations confirm the theoretical part.

This paper deals with the joint estimation of Rayleigh fading channels and symbols in a MC-DS-CDMA system. Formerly, particle filtering has been introduced as a set of promising methods to solve communication problems. PF consists in simulating possible values of the unkwnown parameters and selecting the most likely candidates with regard to the received signal. Here, the Rao-Blackwellized particle filter (RBPF) is used to significantly decrease the variance of the channel/symbol estimates. Our contribution is twofold. Firstly, sinusoidal stochastic models have been shown to better represent the statistical properties of Rayleigh channels than classical autoregressive models. Therefore, the proposed RBPF estimator is based on these models which are expressed as the sum of two sinusoids in quadrature at the maximum Doppler frequency with autoregressive processes as amplitudes. The model parameters are unknown and need to be estimated. Since PFs are not well-suited to recover non-varying parameters, we propose to cross-couple the RBPF with a Kalman filter which makes use of the RBPF ouputs to sequentially update the parameters. Secondly, the choice of an efficient proposal distribution to simulate the particles is crucial for PF performance. We suggest using a suboptimal distribution which simulates likely values of the symbols at a reasonable computational cost.

This paper deals with the joint signal and parameter estimation for linear state-space models. An efficient solution to this problem can be obtained by using a recursive instrumental variable technique based on two dual Kalman filters. In that case, the driving process and the observation noise in the state-space representation for each filter must be white with known variances. These conditions, however, are too strong to be always satisfied in real cases. To relax them, we propose a new approach based on two dual Hinfin filters. Once a new observation of the disturbed signal is available, the first Hinfin algorithm uses the latest estimated parameters to estimate the signal, while the second Hinfin algorithm uses the estimated signal to update the parameters. In addition, as the Hinfin filter behavior depends on the choice of various weights, we present a way to recursively tune them. This approach is then studied in the following cases: (1) consistent estimation of the AR parameters from noisy observations and (2) speech enhancement, where no a priori model of the additive noise is required for the proposed approach. In each case, a comparative study with existing methods is carried out to analyze the relevance of our solution.

This paper deals with a system combining orthogonal frequency di- vision multiplexing (OFDM) and interleave-division multiple access (IDMA). OFDM makes the system robust against intersymbol inter- ference, whereas IDMA combats the multiple access interference. Nevertheless, unwanted phenomena must be taken into account: 1/ carrier frequency offset (CFO) must be estimated/corrected to guarantee the orthogonality between subcarriers and hence the sym- bol detection in the system. 2/ the conventional iterative IDMA receiver, initially proposed by Ping et al., requires a priori knowl- edge of the multipath channel. Therefore, the CFO and the multipath channel must be estimated "accurately" in an OFDM-IDMA system. Our contribution is to propose a new scheme where a CFO correc- tion is no longer necessary, unlike common OFDM approaches. We show that without a CFO correction, the symbols transmitted by the different users can be recovered by modifying the conventional iterative architecture of the IDMA receiver. When considering an OFDM-IDMA network over different Rayleigh fading channels, simulation results clearly show the efficiency of the proposed algorithm in terms of estimation accuracy and bit error rate.

Whereas lecturing is the most widely used mode of instruction, we have explored small-group learning projects to make signal processing more appealing at the University and in Engineering schools in Bordeaux (France). The projects cover a wide range of applications, from audio processing to mobile communication system analysis and can be based on problems suggested by industrial partners. After a state of the art in the area, the students develop signal processing algorithms and usually deliver new softwares. At the end of the semester, they provide a final 8-page report and present their work during a one-day workshop. The projects enable the students to experience cooperative works, which is mostly done in industry. In addition, they help the students to see more easily the links between the courses they follow, including project managing. The students are hence involved in dialog inside their own group, in writing English reports as well as in problem solving, analysis and synthesis. This paper presents four examples dealing with speech processing, spectral analysis, Universal Mobile Telecommunications System (UMTS) mobile positioning and orthogonal frequency division multiple access (OFDMA) synchronization.

In various applications from radar processing to mobile communication systems based on CDMA or OFDM, M-AR multichannel processes are often considered and may be combined with Kalman filtering. However, the estimations of the M-AR parameter matrices and the autocorrelation matrices of the additive noise and the driving process from noisy observations are key problems to be addressed. In this paper, we suggest solving them as an errors-in-variables issue. In that case, the noisy-observation autocorrelation matrix compensated by a specific diagonal block matrix and whose kernel is defined by the M-AR parameter matrices must be positive semi-definite. Hence, the parameter estimation consists in searching every diagonal block matrix that satisfies this property, in reiterating this search for a higher model order and then in extracting the solution that belongs to both sets. A comparative study is then carried out with existing methods including those based on the Extended Kalman Filter (EKF) and the Sigma-Point Kalman Filters (SPKF). It illustrates the relevance and advantages of the proposed approaches.

The paper deals with the local sensitivity analysis of the discrete-time infinite-horizon H2 estimation problem. An improved, nonlinear sensitivity estimate is derived which is less conservative than the existing, condition number based sensitivity estimates.

This study deals with the estimation of a vector process disturbed by an additive white noise. When this process is modelled by a multivariate autoregressive (M-AR) process, optimal filters such as Kalman or H∞ filter can be used for prediction or estimation from noisy observations. However, the estimation of the M-AR parameters from noisy observations is a key issue to be addressed. Off-line or iterative approaches have been proposed recently, but their computational costs can be a drawback. Using on-line methods such as extended Kalman filter and sigma-point Kalman filter are of interest, but the size of the state vector to be estimated is quite high. In order to reduce this size and the resulting computational cost, the authors suggest using dual optimal filters. In this study, the authors propose to extend to the multi-channel case the so-called dual Kalman or H∞ filters-based scheme initially proposed for single-channel applications. The proposed methods are first tested with a synthetic M-AR process and then with an M-AR process corresponding to a mobile fading channel. The comparative simulation study the authors carried out with existing techniques confirms the effectiveness of the proposed methods.

Pour sensibiliser les étudiants au traitement du signal et de l'image, nous avons mis en place des projets personnalisés par groupe de quatre étudiants sur un semestre, à raison d'une demi-journée par semaine. Les sujets proposés par l'équipe pédagogique permettent de couvrir une large gamme d'applications (de l'audio aux systèmes de communications mobiles, de l'image à la vidéo, etc.) et peuvent reposer sur des problématiques industrielles. Ce projet vise à décloisonner les enseignements, à sensibiliser les étudiants à nos thématiques, à les rendre davantage acteurs de leur formation et à leur permettre d'avoir un avant-goût du type d'action qu'ils pourront mener en entreprise. Réalisé en équipe, il constitue un cadre idéal pour confronter l'étudiant à la recherche documentaire et à la gestion de projet. Il permet en outre d'intégrer des enseignements non scientifiques comme l'anglais (au travers de la lecture des documents, la rédaction d'un rapport et d'une soutenance en anglais qui donnent lieu à une évaluation intégrée dans la note finale). Dans cet article, nous illustrons notre démarche pédagogique au travers de trois exemples : le premier porte sur le traitement de la parole, le deuxième sur le traitement d'image et le troisième sur le traitement vidéo.

A great deal of interest has been paid to the time-varying autoregressive (TVAR) parameter tracking, but few papers deal with this issue when noisy observations are available. Recently, this problem was addressed for a TV AR process disturbed by an additive zero-mean white noise, by using deterministic regression methods. In this paper, we focus our attention on the case of an additive colored measurement noise modeled by a moving average process. More particularly, we propose to estimate the TVAR parameters by using a variant of the improved least-squares (lLS) methods, initially introduced by Zheng to estimate the AR parameters from a signal embedded in a white noise. Simulation studies illustrate the advantages and the limits of the approach.

Multicarrier modulation is the common feature of high-data rate mobile wireless systems. In that case, two phenomena disturb the symbol detection. Firstly, due to the relative transmitter-receiver motion and a difference between the local oscillator (LO) frequency at the transmitter and the receiver, a carrier frequency offset (CFO) affects the received signal. This leads to an intercarrier interference (ICI). Secondly, several versions of the transmitted signal are received due to the wireless propagation channel. These unwanted phenomena must be taken into account when designing a receiver. As estimating the multipath channel and the CFO is essential, this PhD deals with several CFO and channel estimation methods based on optimal filtering. Firstly, as the estimation issue is nonlinear, we suggest using the extended Kalman filter (EKF). It is based on a local linearization of the equations around the last state estimate. However, this approach requires a linearization based on calculations of Jacobians and Hessians matrices and may not be a sufficient description of the nonlinearity. For these reasons, we can consider the sigma-point Kalman filter (SPKF), namely the unscented Kalman Filter (UKF) and the central difference Kalman filter (CDKF). The UKF is based on the unscented transformation whereas the CDKF is based on the second order Sterling polynomial interpolation formula. Nevertheless, the above methods require an exact and accurate a priori system model as well as perfect knowledge of the additive measurementnoise statistics. Therefore, we propose to use the H∞ filtering, which is known to be more robust to uncertainties than Kalman filtering. As the state-space representation of the system is non-linear, we first evaluate the “extended H∞ filter”, which is based on a linearization of the state-space equations like the EKF. As an alternative, the “unscented H∞ filter”, which has been recently proposed in the literature, is implemented by embedding the unscented transformation into the “extended H∞ filter” and carrying out the filtering by using the statistical linear error propagation approach. Multicarrier modulation is the common feature of high-data rate mobile wireless systems. In that case, two phenomena disturb the symbol detection. Firstly, due to the relative transmitter-receiver motion and a difference between the local oscillator (LO) frequency at the transmitter and the receiver, a carrier frequency offset (CFO) affects the received signal. This leads to an intercarrier interference (ICI). Secondly, several versions of the transmitted signal are received due to the wireless propagation channel. These unwanted phenomena must be taken into account when designing a receiver. As estimating the multipath channel and the CFO is essential, this PhD deals with several CFO and channel estimation methods based on optimal filtering. Firstly, as the estimation issue is nonlinear, we suggest using the extended Kalman filter (EKF). It is based on a local linearization of the equations around the last state estimate. However, this approach requires a linearization based on calculations of Jacobians and Hessians matrices and may not be a sufficient description of the nonlinearity. For these reasons, we can consider the sigma-point Kalman filter (SPKF), namely the unscented Kalman Filter (UKF) and the central difference Kalman filter (CDKF). The UKF is based on the unscented transformation whereas the CDKF is based on the second order Sterling polynomial interpolation formula. Nevertheless, the above methods require an exact and accurate a priori system model as well as perfect knowledge of the additive measurementnoise statistics. Therefore, we propose to use the H∞ filtering, which is known to be more robust to uncertainties than Kalman filtering. As the state-space representation of the system is non-linear, we first evaluate the “extended H∞ filter”, which is based on a linearization of the state-space equations like the EKF. As an alternative, the “unscented H∞ filter”, which has been recently proposed in the literature, is implemented by embedding the unscented transformation into the “extended H∞ filter” and carrying out the filtering by using the statistical linear error propagation approach.

Recent studies in human health assume a causal link between the complexity of psychophysiological control systems and the complexity of their resulting biosignals. This PhD illustrates the aforementioned principle by relying on an interdisciplinary approach, combining physiology, psychology and signal processing. The dynamics of human output physiological signals are studied in response to induced stress in individual or collective situations. The objective is to extract individual signatures depicting the central and autonomic regulations at rest or in different experimental situations. Since stress is a multifactorial process depending on the individual perception and interpretation of a situation, the study of physiological signals is combined with the evaluation of psychological contextual and dispositional characteristics. We focus our attention on cardiac regulations which are analysed from the time series defined by the successive durations of the RR intervals. Statistical signal processing methods, either temporal, frequency or non-linear, are used to study the adaptive capacities of individuals facing different situations of cognitive tasks associated or not with stressors. A particular interest is given to multiscale entropy to assess the complexity of signals, which makes it possible to consider the interconnections existing between cortical, subcortical structures and autonomic cardiac regulations. The probability density functions of recorded cardiac signals along each different experimental situation are compared two by two by using the Kullback-Leibler divergence, and in particular the estimate of the asymptotic increment of the divergence of Kullback-Leibler. The results show that studying cardiac signals allows to discriminate the psychophysiological state of an individual when facing either cognitive tasks or stressful situations. Psychophysiological state differences emerge during stress, not only at an individual level, but also at a collective one, for which the subject is not directly confronted with stressful stimuli. The stress is therefore empathic. Two experimental applications are carried out from our results. First, we show that the cardiac complexity, which is altered in people stressed at work, can be improved by cardiac coherence biofeedback training. Second, signal processing methods are also used to the study of postural regulation. Overall, our results strengthen the interest of human monitoring in health., Les études récentes en santé humaine supposent un lien de causalité entre la complexité des systèmes de contrôle psychophysiologique et la complexité des biosignaux qu’ils émettent. Le travail mené dans le cadre de cette thèse illustre ce principe en s’appuyant sur une démarche interdisciplinaire, combinant physiologie, psychologie et traitement du signal. Il vise à étudier les dynamiques des signaux physiologiques émis par l’Homme, en réponse à un stress induit en situation individuelle ou collective. Le stress étant un processus multifactoriel qui dépend de la perception et de l’interprétation d’une situation donnée par un individu, l’étude des signaux physiologiques est combinée à l’évaluation de caractéristiques psychologiques contextuelles et dispositionnelles. En particulier, nous nous intéressons aux régulations cardiaques qui sont analysées à partir des séries temporelles définies par les durées successives des intervalles RR. Des approches statistiques temporelles, fréquentielles ou non-linéaires sont utilisées afin d’étudier les capacités d’adaptation des individus confrontés à différentes situations de tâches cognitives associées ou non à des facteurs stressants. Il s’agit d’extraire des signatures caractéristiques des régulations centrales et autonomes, au repos ou dans différentes situations expérimentales. Dans ce travail, un intérêt particulier est accordé à l’entropie multi-échelles afin d’évaluer la complexité des signaux, une complexité induite par les interconnexions existant entre structures corticales, sous-corticales et régulations autonomes cardiaques. Nous proposons également d’analyser les signaux collectés durant les différentes situations expérimentales, en comparant deux à deux leurs densités de probabilité à partir de la divergence de Kullback-Leibler, et en particulier d’une estimation de l'incrément asymptotique de la divergence de Kullback-Leibler. Les résultats obtenus mettent en évidence que l’étude des signaux cardiaques peut permettre d’appréhender l’état psychophysiologique d’un individu lorsqu’il est confronté à des situations de tâches cognitives et de stress. Des différences d’états apparaissent non seulement à l’échelle individuelle, mais également à l’échelle collective, lorsque l’individu n’est pas directement confronté aux stimuli stressants mais que le stress est de nature empathique. Enfin, deux applications sont réalisées. Nous montrons que la complexité des signaux cardiaques, altérée chez des personnes stressées au travail, peut être améliorée par un entraînement à la cohérence cardiaque. Nous appliquons également les méthodes de traitement du signal à l’étude de la régulation posturale. L’ensemble de nos résultats renforcent l’intérêt du monitoring de l’humain en matière de santé.