This work presents an effective and accurate method for determining, from a theoretical and computational point of view, the time-harmonic Green's function of an isotropic elastic half-plane where an impedance boundary condition is considered. This method, based on the previous work done by Durán et al. (cf. [Numer. Math.107 (2007) 295–314; IMA J. Appl. Math.71 (2006) 853–876]) for the Helmholtz equation in a half-plane, combines appropriately analytical and numerical techniques, which has an important...

A theoretically attractive and computationally fast algorithm is presented for the determination of the coefficients of the determinantal polynomial and the coefficients of the adjoint polynomial matrix of a given three-dimensional (3–D) state space model of Fornasini–Marchesini type. The algorithm uses the discrete Fourier transform (DFT) and can be easily implemented on a digital computer.

Le théorème CRT dit comment reconstruire un signal à partir d’un échantillonnage de fréquences parcimonieux. L’hypothèse sur le signal, considéré comme porté par un groupe cyclique d’ordre $N$, est qu’il est porté par un petit nombre de points, $s$, et la méthode est de choisir aléatoirement $CslogN$ fréquences et de minimiser dans l’algèbre de Wiener le prolongement à $\mathbb{Z}/N\mathbb{Z}$ de la transformée de Fourier du signal réduite à ces fréquences. Quand $C$ est grand, la probabilité de reconstruire le signal est voisine...

A method to analyse and filter real-valued discrete signals of finite duration s(n), n=0,1,...,N-1, where $N=2^p$, p>0, by means of time-frequency representation is presented. This is achieved by defining an invertible discrete transform representing a signal either in the time or in the time-frequency domain, which is based on decomposition of a signal with respect to a system of basic orthonormal discrete wavelet functions. Such discrete wavelet functions are defined using the Meyer generating wavelet...