In this paper, we mainly investigate the nonuniform sampling for random signals which are bandlimited in the linear canonical transform (LCT) domain. We show that the nonuniform sampling for a random signal bandlimited in the LCT domain is equal to the uniform sampling in the sense of second order statistic characters after a pre-filter in the LCT domain. Moreover, we propose an approximate recovery approach for nonuniform sampling of random signals bandlimited in the LCT domain. Furthermore, we study the mean square error of the nonuniform sampling. Finally, we do some simulations to verify the correctness of our theoretical results.
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The authors thank the referees very much for carefully reading the paper and for elaborate and valuable suggestions.
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This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 11801256, 11525104 and 11531013).
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Huo, H., Sun, W. Nonuniform sampling for random signals bandlimited in the linear canonical transform domain. Multidim Syst Sign Process 31, 927–950 (2020). https://doi.org/10.1007/s11045-019-00691-2
- Nonuniform sampling
- Linear canonical transform
- Random signals
- Approximate reconstruction
- Sinc interpolation