An adaptive sampling method for high‐dimensional shift‐invariant signals. (27th January 2017)

• Record Type: Journal Article
• Authors: Jiang, Yingchun; Wei, Lusong; Chen, Guangxi
• Is Part Of: Mathematical methods in the applied sciences. Volume 40:Number 12(2017)
• Page Start: 4529
• Page End: 4537
• Publication Date: 2017-01-27
• Subjects: adaptive sampling -- approximate reconstruction -- integrate‐and‐fire sampler -- mobile sampling -- shift‐invariant signals -- high‐dimensional signals; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4323
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, an adaptive method for sampling and reconstructing high‐dimensional shift‐invariant signals is proposed. First, the integrate‐and‐fire sampling scheme and an approximate reconstruction algorithm for one‐dimensional bandlimited signals are generalized to shift‐invariant signals. Then, a high‐dimensional shift‐invariant signal is reduced to be a sequence of one‐dimensional shift‐invariant signals along the trajectories parallel to some coordinate axis, which can be approximately reconstructed by the generalized integrate‐and‐fire sampling scheme. Finally, an approximate reconstruction for the high‐dimensional shift‐invariant signal is obtained by solving a series of stable linear systems of equations. The main result shows that the final reconstructed error is completely determined by the initial threshold in integrate‐and‐fire sampling scheme, which is generally very small. Copyright © 2017 John Wiley & Sons, Ltd.