Choice of sampling interval and extent for finite-energy fields

Date
2017
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Source Title
IEEE Transactions on Signal Processing
Print ISSN
1053-587X
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Publisher
Institute of Electrical and Electronics Engineers Inc.
Volume
65
Issue
7
Pages
1741 - 1751
Language
English
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Abstract

We focus on the problem of representing a nonstationary finite-energy random field, with finitely many samples. We do not require the field to be of finite extent or to be bandlimited. We propose an optimizable procedure for obtaining a finite-sample representation of the given field. We estimate the reconstruction error of the procedure, showing that it is the sum of the truncation errors in the space and frequency domains. We also optimize the truncation parameters analytically and present the resultant Pareto-optimal tradeoff curves involving the error in reconstruction and the sample count, for several examples. These tradeoff curves can be used to determine the optimal sampling strategy in a practical situation based on the relative importance of error and sample count for that application.

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