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

Author

Listed:
  • Yingchun Jiang

    (School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541002, China
    Center for Applied Mathematics of Guangxi (GUET), Guilin 541002, China
    Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin 541002, China)

  • Ni Gao

    (School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541002, China
    Center for Applied Mathematics of Guangxi (GUET), Guilin 541002, China
    Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin 541002, China)

  • Haizhen Li

    (Guilin Institute of Information Technology, Guilin 541002, China)

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.

Suggested Citation

  • Yingchun Jiang & Ni Gao & Haizhen Li, 2024. "Randomized Nonuniform Sampling for Random Signals Bandlimited in the Special Affine Fourier Transform Domain," Mathematics, MDPI, vol. 12(7), pages 1-15, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:7:p:1092-:d:1370573
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