Local Sampling Problems

Abstract

Abstract. The main purpose of this paper is to investigate the local error for the sampling problem in diverse situations. We find that the local error is heavily depending on the asymptotic behavior of the sampling function. By virtue of evaluating the decay of the sampling function, we give a local error estimation for uniform and non-uniform sampling in multiresolution analysis (MRA) and in shift-invariant spaces.

On the Random Sampling Amplitude Error

“…In [3], Atreas et al examined the truncation error of the reconstruction formula in wavelet subspaces. It was not long before Yang et al extended their results to higher dimensional cases and spline-like spaces, e.g., see [12,14]. In this paper we shall investigate the random amplitude error for the above sampling expansions.…”

“…If the sampling points {t j } are dense enough, then {K(t j , •)} constitutes a frame for V 2 (ϕ), and its dual frame { K(t j , •)} is what we try to find, e.g., see [1,13,14,15]. IV) Let ϕ be a scaling function (e.g., see [5,8,9]) satisfying (2) and certain decay and smoothness condition, {V m : m ∈ Z Z} be the multi-resolution analysis generated by ϕ (e.g., see [5]).…”

Breaking chaotic shift key communication via adaptive key identification

“…Since Pecora and Carroll demonstrated chaos synchronization and its potential application to secure communication, [1,2] chaotic secure communication has been an active area of research for the past few years. [3] Chaotic secure communication has evolved into several forms, including chaotic masking, [4] chaotic shift key [5] and chaotic modulation [6] etc.. The development of chaotic secure communication technique followed a path twisting up the hill of security.…”