Sampling measures for the Gabor transform

JOURNAL OF APPROXIMATION THEORY

卷:200

Article

Ascensi, Gerard

关键词: Short-time Fourier transform;    Modulation space;    Sampling sets;    Sampling measures;   

DOI  :  10.1016/j.jat.2015.04.002

来源: Elsevier

【 摘 要 】

Sampling measures of a space H are measures mu such that f vertical bar f vertical bar(p)d mu approximate to parallel to f parallel to(p) for every function f is an element of H. Here we present a study of these measures for the specific case of model spaces of the Gabor transform. These spaces are the continuous transforms v(phi)g of functions g in a modulation space M-p,M-q with respect to a fixed window phi is an element of M-1, the Feichtinger Algebra. We obtain a characterization of these measures in terms of discrete sampling sets and stability results. For a special class of windows that includes most of the important examples of Gabor atoms we also find sufficient conditions in terms of weak limits of uniqueness sets. We also discuss some applications. (C) 2015 Published by Elsevier Inc.

【 授权许可】

Free