An adaptive sampling method for high‐dimensional shift‐invariant signals |
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| Authors: | Yingchun Jiang Lusong Wei Guangxi Chen |
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| Institution: | 1. School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin, China;2. Guangxi Key Laboratory of Cryptography and Information Security, Guilin University of Electronic Technology, Guilin, China;3. Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin, China;4. School of Art and Design, Guilin University of Electronic Technology, Guilin, China |
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| 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. |
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| Keywords: | adaptive sampling approximate reconstruction integrate‐and‐fire sampler mobile sampling shift‐invariant signals high‐dimensional signals |
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