This paper addresses the design of wavelets adapted to the processed signals and the considered application. Our approach consists of parameterizing a mother wavelet, and defining a quality criterion for the optimization of the parameters, according to the context. The first parameterization, leading to orthogonal wavelets, considers the coefficients of the scaling filter as the parameters. A second parameterization, leading to semiorthogonal wavelets, consists of convolving an existing wavelet (or scaling function) by a given sequence. In this paper, we explore these two methods and apply them to the supervised classification of signals made of waveform trains.

We present two improvements/extensions of a previous deterministic blind source separation (BSS) technique, by Belouchrani and Amin, that involves joint-diagonalization of a set of Cohen's class spatial time-frequency distributions. The first contribution concerns the extension of the BSS technique to the stochastic case using spatial Wigner-Ville spectrum. Then, we show that Belouchrani and Amin's technique can be interpreted as a practical implementation of the general equations we provide in the stochastic case. The second contribution is a new criterion aimed at selecting more efficiently the time-frequency locations where the spatial matrices should be joint-diagonalized, introducing single autoterms selection. Simulation results on stochastic time-varying autoregressive moving average (TVARMA) signals demonstrate the improved efficiency of the method.

This paper addresses the problem of time-varying amplitude multichirp signals parameter estimation. We compare two approaches which require a model for the amplitude. First, we use a basis of time-localized functions associated with Bayesian estimation. Secondly, we use an autoregressive model associated with a mixed high-order ambiguity function/Kalman filter estimation. Results show that both methods are efficient to solve this estimation problem.

We present a robust method for time-frequency model estimation. It involves a robust Leclerc's estimator to ensure robustness w.r.t. noise and interferences present in time- frequency representations. This scheme is applied to fish age and growth analysis from otolith images. This application involves the estimation of the parameters of a priori fish growth models using this robust time-frequency analysis. We present a quantitative experimental validation over a large set of real images of Plaice otoliths.

This paper addresses the problem of classifying chirp signals using hierarchical Bayesian learning combined with Markov Chain Monte Carlo (MCMC) methods. Bayesian learning consists of estimating the distribution of observed data conditional upon each class from a set of training samples. Unfortunately, this estimation often requires to evaluate intractable multidimensional integrals. This paper studies an original implementation of hierarchical Bayesian learning which estimates the class conditional probability densities using MCMC methods. The performance of this implementation is compared to other existing approaches for the classification of chirp signals.

This paper addresses supervised signal classification using discrete time-scale representations. Given a set of learning signals and a class of discrete wavelet-basis, we propose to select the mother wavelet which yields the best classification results. This corresponds to determining the filter (used for the decomposition) that is ideally adapted to the specific classification problem at hand. It is realized by optimizing the filter coefficients according to a contrast criterion calculated on the learning set. Simulations show the efficiency of this approach.

This paper addresses the problem of loudspeaker testing. Two applications are investigated: loudspeaker manufacturing fault detection and maintenance. In order to comply with practical requirements, we propose a new, brief, nonstationary test signal. Recorded loudspeaker responses are processed using an improved time-frequency decision algorithm. The fault detection procedure is tested with real data. The results show its accuracy and practical interest.

Time-frequency representations (TFRs) are efficient tools for nonstationary signal classification. However, the choice of the TFR and of the distance measure employed is critical when no prior information other than a learning set of limited size is available. In this letter, we propose to jointly optimize the TFR and distance measure by minimizing the (estimated) probability of classification error. The resulting optimized classification method is applied to multicomponent chirp signals and real speech records (speaker recognition). Extensive simulations show the substantial improvement of classification performance obtained with our optimization method.

This paper addresses the problem of supervised classification using general Bayesian learning. General Bayesian learning consists of estimating the unknown class-conditional densities from a set of labelled samples. However, the estimation requires to evaluate intractable multidimensional integrals. This paper studies an implementation of general Bayesian learning based on Markov chain Monte Carlo (MCMC) methods.

This paper presents a new method based on time frequency representations (TFRs) for detecting abrupt changes in non-stationary noisy signals, Stationarity indices (SIs), based on different distance measures between TFRs, are defined and a comparison of the performances is performed using ROC curves and statistical properties. Two sets of signals are specially studied here: signals presenting very short segments and nonstrictly stepwise stationary signals. For these signals, classical methods based on autoregressive (AR) spectral estimators are often unsuccessful.

The paper presents a new method based on time-frequency representations (TFRs) for detecting reflex activities in EMG signals of biceps brachii. A perturbed flexion-extension forearm movement in the horizontal plane is studied here and a stationarity index is defined using TFRs of Cohen's group in order to depict the reaction of the subject to the perturbation.

The goal of the work described is to provide an estimation algorithm of the dynamics of a mobile robot. The measured variables are the control laws of the motors and the angles between the robot principal axis and a lot of fixed beacons, given by a rotative onboard camera. The specific problems are of several types: the motion of the robot is described by a continuous-time nonlinear equation. The measures are uncadenced and nonlinear (angles). The state of the robot is not observable by a single measure. So a specific continuous/discrete-time extended Kalman filter with measurement reconstruction is developed.>

A method is proposed which solves the problem of the Bayes classification of ARMA (autoregressive moving average) signals when the models of classes and samples are not exactly known but only estimated from finite-length data sequences. Justified approximations and the hypothesis lead to decision rules including the variances of the estimations. The results obtained on a large set of simulated data show that this approach is superior to the best classical methods (cepstral distance or Kullback divergence), particularly in the common case where the hypothesis of those methods is not verified (short samples. small training sets. random classes).>