Messaoud Benidir

Some properties of lattice autoregressive filters

An autoregressive filter is defined either by the components of the regression vector or by the reflection coefficients appearing in its lattice representation. The mathematical expression of the regression vector in terms of the reflection coefficients is very complex but many structural properties can be obtained without this exact expression. In this paper, we present some examples of such structural properties, and we apply these results to prove some extremal properties of stable filters such as the maximum value of the components of the regression vector or the maximum value of its norm. Moreover, some properties of the boundary of the stability domain are discussed.

Blind separation of impulsive alpha-stable sources using minimum dispersion criterion

This letter introduces a novel blind source separation (BSS) approach for extracting impulsive signals from their observed mixtures. The impulsive signals are modeled as real-valued symmetric alpha-stable (S/spl alpha/S) processes characterized by infinite second- and higher-order moments. The proposed approach uses the minimum dispersion (MD) criterion as a measure of sparseness and independence of the data. A new whitening procedure by a normalized covariance matrix is introduced. We show that the proposed method is robust, so-named for the property of being insensitive to possible variations in the underlying form of sampling distribution. Algorithm derivation and simulation results are provided to illustrate the good performance of the proposed approach. The new method has been compared with three of the most popular BSS algorithms: JADE, EASI, and restricted quasi-maximum likelihood (RQML).

Multiresolution wavelet-based QRS complex detection algorithm suited to several abnormal morphologies

The electrocardiogram (ECG) signal is considered as one of the most important tools in clinical practice in order to assess the cardiac status of patients. In this study, an improved QRS (Q wave, R wave, S wave) complex detection algorithm is proposed based on the multiresolution wavelet analysis. In the first step, high frequency noise and baseline wander can be distinguished from ECG data based on their specific frequency contents. Hence, removing corresponding detail coefficients leads to enhance the performance of the detection algorithm. After this, the authors method is based on the power spectrum of decomposition signals for selecting detail coefficient corresponding to the frequency band of the QRS complex. Hence, the authors have proposed a function g as the combination of the selected detail coefficients using two parameters λ 1 and λ 2, which correspond to the proportion of the frequency ranges of the selected detail compared with the frequency range of the QRS complex. The proposed algorithm is evaluated using the whole arrhythmia database. It presents considerable capability in cases of low signal-to-noise ratio, high baseline wander and abnormal morphologies. The results of evaluation show the good detection performance; they have obtained a global sensitivity of 99.87%, a positive predectivity of 99.79% and a percentage error of 0.34%.

Extensions of the stability criterion for ARMA filters

Using the lattice representation of an ARMA filter, it is well known that the necessary and sufficient condition so that the poles are inside the unit circle is |k_{i} where the k i s are the reflection coefficients. The filter is said to be wide sense stable if no pole is located outside the unit circle, and it is interesting to characterize this stability by an appropriate necessary and sufficient condition. To establish this condition, the concept of canonical reflection coefficient is introduced, which eliminates the problems appearing when the Levinson recursion is not inversible. Some examples are discussed and a simple and practical test for wide sense stability is given.

Comparison between some stability criteria of discrete-time filters

Rouths algorithm is written in the form of polynomial recursion and transposed for testing stability in the wide sense of discrete-time linear systems. The algorithm obtained is a three-term recursion of symmetric polynomials. This recursion easily gives both the coefficients appearing in the continued fraction expansion associated to a given polynomial in the z-domain, and a computation scheme for the bilinear transformation of polynomials. Finally, this recursion is compared to other algorithms already known for testing stability. >

On the selection of Intrinsic Mode Function in EMD method: Application on heart sound signal

Empirical mode decomposition (EMD) allows decomposing an observed multicomponent signal into a set of monocomponent signals called Intrinsic Mode Functions (IMFs). EMD provides a large number of IMFs and it is important to select the fundamental IMFs and eliminate the redundant ones. This paper proposes a new criterion, based simultaneously on the Minkowski distance and the Jensen Rényi divergence of order α (α-JRD), to automatically select the appropriate IMFs in a set of the extracted ones. Examples, using synthetic and real-life heart sound signals, are presented in order to validate the performance of the proposed technique.

SAR imaging using multidimensional continuous wavelet transform and applications to polarimetry and interferometry

Usual SAR imaging process makes the assumption that the reflectors are isotropic and white (i.e., they behave in the same way regardless the angle from which they are viewed and the emitted frequency within the bandwidth). The multidimensional continuous wavelet transform (CWT) in radar imaging was initially developed to highlight the image degradations due to these assumptions. In this article the wavelet transform method is widened to polarimetry and interferometry fields. The wavelet tool is first used for polarimetric image enhancement, then for coherence optimization in interferometry. This optimization by wavelets, compared with the polarimetric one, gives better results on the coherence level. Finally, a combination of both methods is proposed.

Distinction between polynomial phase signals with constant amplitude and random amplitude

In this paper we propose to distinguish between constant amplitude polynomial phase signals and the ones having random amplitude. We study four possibilities for the modulating process. We show that the distinction of this kind of signals is not always possible when using the polynomial phase transform. In fact, in some applications, we show that we cannot estimate the phase of the signal with this transform. In order to solve this problem, we introduce a new transform which allows us to estimate this phase in these particular situations. The obtained transform is referred to as the modified polynomial phase transform.

Denoising and characterization of heart sound signals using optimal intrinsic mode functions

Empirical mode decomposition (EMD) allows decomposing an observed multicomponent signal into a set of monocomponent signals, called Intrinsic Mode Functions (IMFs). The aim of this paper is to characterize some heart sound (HS) signals embedded in noise using the EMD approach. In particular, the proposed technique automatically selects the most appropriate IMFs achieving the denoising based on EMD and Euclidean measure. Synthetic and real-life signals are used in the various examples to validate, and demonstrate the effectiveness, of the proposed method. Furthermore, this technique is compared to the commonly known approach based on the noise model.

On the root distribution of general polynomials with respect to the unit circle

A modification and an extension of Schur-Cohns algorithm and Jurys table are presented. The new versions of the classical algorithms allow us to associate a sequence of coefficients kj to every polynomial P. We establish that the number of zeros of P outside the unit circle equals the number of kj satisfying ¦kj¦ > 1. A simple expression for the number of zeros of P on the unit circle is also established. An extension of the modified algorithm which introduces an arbitrary parameter allows us to study the critical situations: 1 − e ⩽ ¦kj¦ ⩽ 1 + e, where e is an arbitrary small positive number.