Frames in spaces with finite rate of innovation |
| |
Authors: | Qiyu Sun |
| |
Institution: | (1) Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA |
| |
Abstract: | Signals with finite rate of innovation are those signals having finite degrees of freedom per unit of time that specify them.
In this paper, we introduce a prototypical space modeling signals with finite rate of innovation, such as stream of (different) pulses found in GPS applications, cellular
radio and ultra wide-band communication. In particular, the space is generated by a family of well-localized molecules of similar size located on a relatively separated set using coefficients, and hence is locally finitely generated. Moreover that space includes finitely generated shift-invariant spaces, spaces of non-uniform splines, and the twisted shift-invariant space
in Gabor (Wilson) system as its special cases. Use the well-localization property of the generator , we show that if the generator is a frame for the space and has polynomial (sub-exponential) decay, then its canonical dual (tight) frame has the same polynomial (sub-exponential)
decay. We apply the above result about the canonical dual frame to the study of the Banach frame property of the generator
for the space with , and of the polynomial (sub-exponential) decay property of the mask associated with a refinable function that has polynomial
(sub-exponential) decay.
|
| |
Keywords: | frame Banach frame localized frame signals with finite rate of innovation space of homogenous type matrix algebra refinable function wavelets |
本文献已被 SpringerLink 等数据库收录! |
|