Yves Grenier

Time-dependent ARMA modeling of nonstationary signals

Modeling of nonstationary signals can be achieved through time-dependent autoregressive moving-average models and lattices, by the use of a limited series expansion of the time-varying coefficients in the models. This method leads to an extension of several well-known techniques of stationary spectral estimation to the nonstationary case. Time-varying AR models are identified by means of a fast (Levinson) algorithm which is also suitable for the AR part of a mixed ARMA model. An alternative to this method is given by the extension of Cadzows method. Lattices with time-dependent reflection coefficients are identified through an algorithm which is similar to Burgs. Finally, the Prony-Pisarenko estimator is adapted to this nonstationary context, the signal considered in this case being the output of a zero-input time-varying system corrupted by an additive white noise. In all these methods the estimation is global in the sense that the parameters are estimated over a time interval [0, T], given the observations [y 0 ... y T ]. The maximum likelihood method which falls within the same framework is also briefly studied in this paper. Simulations of these algorithms on chirp signals and on transitions between phonemes in speech conclude the paper.

A signal subspace tracking algorithm for microphone array processing of speech

This paper presents a method of adaptive microphone array beamforming using matched filters with signal subspace tracking. Our objective is to enhance near-field speech signals by reducing multipath and reverberation. In real applications such as speech acquisition in acoustic environments, sources do not propagate along known and direct paths. Particularly in hands-free telephony, we have to deal with undesired propagation phenomena such as reflections and reverberation. Prior methods developed adaptive microphone arrays for noise reduction after a time delay compensation of the direct path. This simple synchronization is insufficient to produce an acceptable speech quality, and makes adaptive beamforming unsuitable. We prove the identification of source-to-array impulse responses to be possible by subspace tracking. We consequently show the advantage of treating synchronization as a matched filtering step. Speech quality is indeed enhanced at the output by the suppression of reflections and reverberation (i.e., dereverberation), and efficient adaptive beamforming for noise reduction is applied without risk of signal cancellation. Evaluations confirm the performance achieved by the proposed algorithm under real conditions.

Underdetermined Blind Separation of Nondisjoint Sources in the Time-Frequency Domain

This paper considers the blind separation of nonstationary sources in the underdetermined case, when there are more sources than sensors. A general framework for this problem is to work on sources that are sparse in some signal representation domain. Recently, two methods have been proposed with respect to the time-frequency (TF) domain. The first uses quadratic time-frequency distributions (TFDs) and a clustering approach, and the second uses a linear TFD. Both of these methods assume that the sources are disjoint in the TF domain; i.e., there is, at most, one source present at a point in the TF domain. In this paper, we relax this assumption by allowing the sources to be TF-nondisjoint to a certain extent. In particular, the number of sources present at a point is strictly less than the number of sensors. The separation can still be achieved due to subspace projection that allows us to identify the sources present and to estimate their corresponding TFD values. In particular, we propose two subspace-based algorithms for TF-nondisjoint sources: one uses quadratic TFDs and the other a linear TFD. Another contribution of this paper is a new estimation procedure for the mixing matrix. Finally, then numerical performance of the proposed methods are provided highlighting their performance gain compared to existing ones

A microphone array for car environments

Abstract This paper describes a microphone array for speech recording in car environments. The array is designed for hands-free radiotelephone, and is also used as a front-end for an automatic speech recognition system (this study has been realised within the european ESPRIT project ARS “adverse environment recognition of speech”). We first summarise the adaptive beamforming techniques that we have used. We then describe several aspects of the implementation of the array (configuration, design of fixed beamformers, adaptation, complexity reduction). In the last section, we evaluate the performance of the array. Two measures of performance have been retained, one is the signal-to-noise ratio, and the other is the score obtained with the speech recognition system.

The generalized multidelay adaptive filter: structure and convergence analysis

Frequency-domain adaptive filters have long been recognized as an attractive alternative to time-domain algorithms when dealing with systems with large impulse response and/or correlated input. New frequency-domain LMS adaptive schemes have been proposed. These algorithms essentially retain the attractive features of frequency-domain implementations, while requiring a processing delay considerably smaller than the length of the impulse response. The authors show that these algorithms can be seen as particular implementations of a more general scheme, the generalized multidelay filter (GMDF). Within this general class of algorithms, we focus on implementations based on the weighted overlap and add reconstruction algorithms; these variants, overlooked in previous contributions, provide an independent control of the overall processing delay and of the rate of update of the filter coefficients, allowing a trade-off between the computational complexity and the rate of convergence. We present a comprehensive analysis of the performance of this new scheme and to provide insight into the influence of impulse response segmentation on the behavior of the adaptive algorithm. Exact analytical expressions for the steady-state mean-square error are first derived. Necessary and sufficient conditions for the convergence of the algorithm to the optimal solution within finite variance are then obtained, and are translated into bounds for the stepsize parameter. Simulations are presented to support our analysis and to demonstrate the practical usefulness of the GMDF algorithm in applications where large impulse response has to be processed. >

A multichannel affine projection algorithm with applications to multichannel acoustic echo cancellation

A straightforward generalization of the so-called affine projection algorithm (APA) to the multichannel (MC) case is easily obtained. However, due to the strong correlation between the input signals of the various channels, the resulting algorithm converges very slowly. The article describes the way to overcome this problem and derives an efficient algorithm that makes use of additional orthogonal projections.

An algorithm for multisource beamforming and multitarget tracking

A new algorithm for simultaneous robust multisource beamforming and adaptive multitarget tracking is proposed. Self-robustness to locations errors or variations is introduced by a source-subspace-based tracking procedure of steering vectors in the array manifold. This LMS-type procedure is generalized from a former work we developed in the single source case. Two beamforming structures are actually proposed. The first is adaptive and optimal for uncorrelated sources and correlated noise. The second is conventional and optimal for correlated sources and uncorrelated white noise. The proposed algorithm and MUSIC show an identical asymptotic variance in localization for immobile sources, whereas for the mobile case, the proposed algorithm is highly advantageous. Then, it is shown that the additional use of some kinematic parameters (i.e., speed, acceleration, etc.) inferred from the reconstructed trajectories improves the tracking performance and overcomes some of the problems of crossing targets. The efficiency of multitarget tracking and the robustness of multisource beamforming are proved and then confirmed by simulation. The number of sources can be initialized and tracked by a marginal proposed procedure. The beamforming performance is shown to be optimal as the single source case. Finally, the algorithm has a very low order of arithmetic complexity.

Blind Separation of Underdetermined Convolutive Mixtures Using Their Time–Frequency Representation

This paper considers the blind separation of nonstationary sources in the underdetermined convolutive mixture case. We introduce, two methods based on the sparsity assumption of the sources in the time-frequency (TF) domain. The first one assumes that the sources are disjoint in the TF domain, i.e., there is at most one source signal present at a given point in the TF domain. In the second method, we relax this assumption by allowing the sources to be TF-nondisjoint to a certain extent. In particular, the number of sources present (active) at a TF point should be strictly less than the number of sensors. In that case, the separation can be achieved thanks to subspace projection which allows us to identify the active sources and to estimate their corresponding time-frequency distribution (TFD) values. Another contribution of this paper is a new estimation procedure for the mixing channel in the underdetermined case. Finally, numerical performance evaluations and comparisons of the proposed methods are provided highlighting their effectiveness.

Parametric Time-Frequency Representations

This text describes parametric time-frequency representations, called here reliefs. After an analysis of the properties expected for such a relief, the classes of nonstationary signals are studied. One observe several equivalences between various definitions. This permits to define the class for which the concept of relief will be valid: the class of harmonizable nondegenerate signals. Two reliefs are presented in details, one defined by Priestley for oscillatory signals, the other defined by Tjostheim using a commutation relation between two operators representing time and frequency. A third relief is also discussed: the rational relief. It is more adequate and simpler to use for ARMA signals. The estimation of these reliefs is also considered, through time-dependent ARMA modelling.

A fast two-channel projection algorithm for stereophonic acoustic echo cancellation

We propose a new fast projection algorithm for stereophonic acoustic echo cancellation. This algorithm can be viewed as a generalization of the extended two-channel LMS algorithm which takes into account the correlation between the input signals. Moreover, this algorithm fits naturally with the framework of affine projection techniques extended to the two-channel case. Its computational complexity is less than half the complexity of the fastest two-channel RLS versions. Simulation results show the obtained performance.