Frames in spaces with finite rate of innovation

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 Vq(, ) modelling 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 Vq(, ) is generated by a family of well-localized molecules of similar size located on a relatively-separated set using q coefficients, and hence is locally finitely-generated. Moreover that space Vq(, ) 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 V2(, ) and has polynomial (subexponential) decay, then its canonical dual (tight) frame has the same polynomial (subexponential) decay....

• Type: Journal
• Year: 2008
• Where: ADCM
• Authors: Qiyu Sun
• Keywords: ADCM 2008, Finite Rate, Shift-invariant Space, Space