Perturbed sampling formulas and local reconstruction in shift invariant spaces

AbstractLet Vϕ be a closed subspace of L2(R) generated from the integer shifts of a continuous function ϕ with a certain decay at infinity and a non-vanishing property for the function Φ†(γ)=∑n∈Zϕ(n)e−inγ on [−π,π]. In this paper we determine a positive number δϕ so that the set {n+δn}n∈Z is a set of stable sampling for the space Vϕ for any selection of the elements δn within the ranges ±δϕ. We demonstrate the resulting sampling formula (called perturbation formula) for functions f∈Vϕ and also we establish a finite reconstruction formula approximating f on bounded intervals. We compute the corresponding error and we provide estimates for the jitter error as well

Signal Analysis on Strings for Immune-Type Pattern Recognition

We use wavelet-type discrete transforms for signal analysis on strings of finite length. We apply these transforms for edge and hidden Markov process detection. We also present new approaches for string matching and for measures of the diversity of chaotic strings