Average sampling and reconstruction for reproducing kernel stochastic signals. (8th October 2015)

• Record Type: Journal Article
• Authors: Jiang, Yingchun; Wang, Suping; Yang, Meixiang
• Is Part Of: Mathematical methods in the applied sciences. Volume 39:Number 11(2016:Jul. 30)
• Page Start: 2930
• Page End: 2938
• Publication Date: 2015-10-08
• Subjects: stochastic signals -- reproducing kernel space -- average sampling -- mean square convergence; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3740
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : This paper mainly considers the problem of reconstructing a reproducing kernel stochastic signal from its average samples. First, a uniform convergence result for reconstructing the deterministic reproducing kernel signals by an iterative algorithm is established. Then, we prove that the quadratic sum of the corresponding reconstructed functions is uniformly bounded. Moreover, the reconstructed functions provide a frame expansion in the special case p = 2. Finally, the mean square convergence for recovering a weighted reproducing kernel stochastic signal from its average samples is given under some decay condition for the autocorrelation function, which can be removed for the case p = 2. Copyright © 2015 John Wiley & Sons, Ltd.