The compatibility of unsynchronized interleaved uniform sampling with Sigma-Delta analog-to-digital conversion is investigated. Let f be a bandlimited signal that is sampled on a collection of N interleaved grids  {kT + Tn} k ∈ Zwith offsets ${\left\{T_n\right\}}_{n=1}^N\subset [0,T]$ T n n = 1 N ⊂ [ 0 ,T ] . If the offsetsTn are chosen independently and uniformly at random from  [0,T]  and if the sample values of fare quantized with a first order Sigma-Delta algorithm, then with high probability the quantization error $|f\left(t\right)-\tilde{f}\left(t\right)|$ | f ( t ) − x10ff65;...

The compatibility of unsynchronized interleaved uniform sampling with Sigma-Delta analog-to-digital conversion is investigated. Let f be a bandlimited signal that is sampled on a collection of N interleaved grids  {kT + Tn} k ∈ Z with offsets ${\left\{T_n\right\}}_{n=1}^N\subset [0,T]$. If the offsets Tn are chosen independently and uniformly at random from  [0,T]  and if the sample values of f are quantized with a first order Sigma-Delta algorithm, then with high probability...

Dans cet article, nous reprenons une méthode due à Ingrid Daubechies pour générer des bases orthonormales de fonctions dans L2(R) de la forme {2j/2 ψ (2jx - k)}j,k ∈ Z à partir de filtres miroir en quadrature (QMF) tels que l'ondelette ψ ait de bonnes propriétés de régularité. Une estimation de l'exposant de Hölder global optimal est obtenue en caractérisant précisément la decroissance de la fonction ψ'. Nous précisons finalement les liens exacts entre la régularité de l'ondelette et son ordre de...

By means of simple computations, we construct new classes of non separable QMF's. Some of these QMF's will lead to non separable dyadic compactly supported orthonormal wavelet bases for L2(R2) of arbitrarily high regularity.