Sampling streams of pulses with unknown shapes
File(s)
Accepted version
Author(s)
Zhang, Y
Dragotti, P-L
Type
Journal Article
Abstract
This paper extends the class of continuous-time signals that can be perfectly reconstructed by developing a theory for the sampling and exact reconstruction of streams of short pulses with unknown shapes. The single pulse is modelled as the delayed version of a wavelet-sparse signal, which is normally not band limited. As the delay can be an arbitrary real number, it is hard to develop an exact sampling result for this type of signals. We achieve the exact reconstruction of the pulses by using only the knowledge of the Fourier transform of the signal at specific frequencies. We further introduce a multi-channel acquisition system which uses a new family of compact-support sampling kernels for extracting the Fourier information from the samples. The shape of the kernel is independent of the wavelet basis in which the pulse is sparse and hence the same acquisition system can be used with pulses which are sparse on different wavelet bases. By exploiting the fact that pulses have short duration and that the sampling kernels have compact support, we finally propose a local and sequential algorithm to reconstruct streaming pulses from the samples.
Date Issued
2016-06-27
Date Acceptance
2016-06-10
Citation
IEEE Transactions on Signal Processing, 2016, 64 (20), pp.5450-5465
ISSN
1053-587X
Publisher
IEEE
Start Page
5450
End Page
5465
Journal / Book Title
IEEE Transactions on Signal Processing
Volume
64
Issue
20
Copyright Statement
© 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Sponsor
Commission of the European Communities
Grant Number
277800
Subjects
Science & Technology
Technology
Engineering, Electrical & Electronic
Engineering
Wavelets
sampling
sparsity
FINITE-RATE
SIGNAL RECONSTRUCTION
SPIKE DETECTION
INNOVATION
INFORMATION
PRINCIPLES
MOMENTS
Networking & Telecommunications
MD Multidisciplinary
Publication Status
Published