Paper Info
Title
Recovery of Bandlimited Signals in Linear Canonical Transform Domain from Noisy Samples
Abstract
The linear canonical transform (LCT) has been shown to be a useful and powerful tool for signal processing and optics. Many reconstruction strategies for bandlimited signals in LCT domain have been proposed. However, these reconstruction strategies can work well only if there are no errors associated with the numerical implementation of samples. Unfortunately, this requirement is almost never satisfied in the real world. To the best of the author's knowledge, the statistical problem of LCTed bandlimited signal recovery in the presence of random noise still remains unresolved. In this paper, the problem of recovery of bandlimited signals in LCT domain from discrete and noisy samples is studied. First, it is shown that the generalized Shannon-type reconstruction scheme for bandlimited signals in LCT domain cannot be directly applied in the presence of noise since it leads to an infinite mean integrated square error. Then an orthogonal and complete set for the class of bandlimited signals in LCT domain is proposed; and further, an oversampled version of the generalized Shannon-type sampling theorem is derived. Based on the oversampling theorem and without adding too much complexity, a reconstruction algorithm for bandlimited signals in LCT domain from discrete and noisy observations is set up. Moreover, the convergence of the proposed reconstruction scheme is also proved. Finally, numerical results and potential applications of the proposed reconstruction algorithm are given.
Year
DOI
Venue
2014
10.1007/s00034-013-9723-z
Circuits, Systems, and Signal Processing
Keywords
Field
DocType
Recovery algorithm, Bandlimited signal, Linear canonical transform, Random noise
Convergence (routing),Signal processing,Mathematical optimization,Oversampling,Bandlimiting,Random noise,Reconstruction algorithm,Nyquist–Shannon sampling theorem,Nyquist rate,Mathematics
Journal
Volume
Issue
ISSN
33
6
1531-5878
Citations 
PageRank 
References 
3
0.39
19
Authors
3
Name
Order
Citations
PageRank
Hui Zhao1315.15
Ruyan Wang224140.80
Daiping Song3263.01