The sampling theorem for non homogeneous random field in the n-dimensional separable linear canonical transform domain

Shuo Zhang and Suping Wang

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 24, 7840-7861

Abstract: In this article, we extend the famous Shannon sampling theorem for non homogeneous random fields in the n-dimensional separable linear canonical transform (n-D SLCT) domain with a new idea. The first is the theoretical framework for n-D SLCT domain. Second, we present the sampling theorems for multivariate continuous signals and non homogeneous random fields bandlimited in the n-D SLCT domain and establish a condition for a wide class of random fields to be determined by their samples in the mean square sense. Third, we analyze the sampling truncation error estimation for a non homogeneous random field in the n-D SLCT domain. Fourth, the sampling approximation for a random field in the almost sure sense in the n-D SLCT domain is analyzed. Finally, the simulations are shown to verify the feasibility of the result.

Date: 2025
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DOI: 10.1080/03610926.2025.2483571

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