Title :
Frames and sampling theorems for translation-invariant subspaces
Author :
Zhao, Ping ; Liu, Guizhong ; Zhao, Chun
Author_Institution :
Dept. of Inf. & Commun. Eng., Xi´´an Jiaotong Univ., China
Abstract :
A sampling theorem for frames in translation-invariant subspaces of L2(R) is established, which is a generalization of a result of W. Chen and S. Itoh for Riesz bases (see IEEE Trans. Sig. Processing, vol.46, p.2822-4, 1998). Then, some necessary conditions for sampling are derived for Riesz bases. Some relationships and properties are also derived about the relevant functions.
Keywords :
signal sampling; wavelet transforms; Riesz bases; Shannon sampling theorem; digital communication theory; digital signal processing theory; frames theorem; signal analysis; translation-invariant subspaces; wavelets; Digital signal processing; Equations; Fourier transforms; Image processing; Image sampling; Sampling methods; Signal analysis; Signal processing; Signal sampling; Sufficient conditions;
Journal_Title :
Signal Processing Letters, IEEE
DOI :
10.1109/LSP.2003.819357
