Randomized Nonuniform Sampling for Random Signals Bandlimited in the Special Affine Fourier Transform Domain

Yingchun Jiang, Ni Gao and Haizhen Li ()
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Yingchun Jiang: School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541002, China
Ni Gao: School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541002, China
Haizhen Li: Guilin Institute of Information Technology, Guilin 541002, China

Mathematics, 2024, vol. 12, issue 7, 1-15

Abstract: The nonuniform sampling and reconstruction of bandlimited random signals in the SAFT domain is discussed in the paper, where the nonuniform samples are obtained by randomly disturbing the uniform sampling. First, we prove that the concerned nonuniform problem is equivalent to the process of uniform sampling after a prefilter in the statistic sense. Then, an approximate reconstruction method based on sinc interpolation is proposed for the randomized nonuniform sampling of SAFT-bandlimited random signals. Finally, we offer the mean square error estimate for the corresponding approximate recovery approach. The results generalize the conclusions of nonuniform sampling of bandlimited random signals in the FrFT and LCT domains to the SAFT domain.

Keywords: special affine Fourier transform; randomized nonuniform sample; bandlimited random signals; mean square error estimate; approximate recovery (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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