Discrete-time multi-scale systems

We introduce multi-scale filtering by the way of certain double convolution systems. We prove stability theorems for these systems and make connections with function theory in the poly-disc. Finally, we compare the framework developed here with the white noise space framework, within which a similar class of double convolution systems has been defined earlier

Parameter estimation via differential algebra and operational culculus

Parameter estimation is approached via a new standpoint, based on differential algebra and operational calculus. Some applications such as, the estimation of a noisy damped sinusoid, the analysis of chirp signal, the detection of piecewise polynomial signals and their discontinuities are presented with numerical simulations

A character-automorphic Hardy spaces approach to discrete-time scale-invariant systems

We define the scale translation in discrete-time via the action of the group of automorphisms of the disk. Two important tools that we will use are the theory of automorphic functions and the theory of reproducing kernel Hilbert spaces. When the group is Fuchsian and of Widom type, we present a class of signals and systems which are both discrete-scale and discrete-time stationary. Finally a class of digital self-similar signals and systems is presented

A Volterra filter for neuronal spike detection

The spike detection problem is cast into a delay estimation. Using elementary operational calculus, we obtain an explicit characterization of the spike locations, in terms of short time window iterated integrals of the noisy signal. From this characterization, we derive a joint spike detection and localization system where the decision function is implemented as the output of a digital Volterra filter. Simulation results using experimental data shows that the method compares favorably with one of the most successful one in the litterature

Algebraic Change-Point Detection

Elementary techniques from operational calculus, differential algebra, and noncommutative algebra lead to a new approach for change-point detection, which is an important field of investigation in various areas of applied sciences and engineering. Several successful numerical experiments are presented

Transformée en échelle de signaux stationnaires

International audienceUsing the scale transform of a discrete time signal we define a new family of linear systems. We focus on a particular case related to function theory in the bidisk

Sur la résolution de l'identité de Bezout pour l'égalisation autodidacte de systèmes mono-entrée-multi-sorties

Nous présentons une approche polynomiale pour le problème de l'égalisation autodidacte de système multicanal, à réponse impulsionnelle finie. Cette approche utilise une identification entrée-sortie de système, que l'on peut interpréter comme une prédiction linéaire spatio-temporelle puis, une résolution directe de l'identité de Bezout, sous-jacent au problème d'égalisation. En l'abscence de bruit, on montre que le nombre de coefficients non nuls de la réponse combinée canal-égaliseur n'excède pas N - N' +1 où NetN' sont les longueurs du canal et de l'égaliseur. Dans le cas surmodélisé, on montre que cette réponse s'annulle

Numerical differentiation with annihilators in noisy environment

International audienceNumerical differentiation in noisy environment is revised through an algebraic approach. For each given order, an explicit formula yielding a pointwise derivative estimation is derived, using elementary differential algebraic operations. These expressions are composed of iterated integrals of the noisy observation signal. We show in particular that the introduction of delayed estimates affords significant improvement. An implementation in terms of a classical finite impulse response (FIR) digital filter is given. Several simulation results are presented

Algebraic Parameter Estimation of Damped Exponentials

International audienceThe parameter estimation of a sum of exponentials or the exponential fitting of data is a well known problem with a rich history. It is a nonlinear problem which presents several difficulties as the ill-conditioning when roots have close values and the order of the estimated parameters, among others. One of the best existing methods is the modified Prony algorithm which suffers in the presence of noise. In this paper we propose an algebraic method for the parameter estimation. The method, differently from the modified Prony method, is considerably robust to noise. The comparison of both through simulations confirm the good performance of the algebraic method

A delay estimation approach to change-point detection

The change-point detection problem is cast into a delay estimation. Using a local piecewise polynomial representation and some elementary algebraic manipulations, we give an explicit characterization of a change-point as a solution of a given polynomial equation. A key feature of this polynomial equation is its coefficients being composed by short time window iterated integrals of the noisy signal. The so designed change-point detector shows good robustness to various type of noises