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Sampling and distortion tradeoffs for bandlimited periodic signals

Mohammadi, E ; Sharif University of Technology | 2018

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  1. Type of Document: Article
  2. DOI: 10.1109/TIT.2017.2782754
  3. Publisher: Institute of Electrical and Electronics Engineers Inc , 2018
  4. Abstract:
  5. In this paper, the optimal sampling strategies (uniform or nonuniform) and distortion tradeoffs for Gaussian bandlimited periodic signals with additive white Gaussian noise are studied. Our emphasis is on characterizing the optimal sampling locations as well as the optimal presampling filter to minimize the reconstruction distortion. We first show that to achieve the optimal distortion, no presampling filter is necessary for any arbitrary sampling rate. Then, we provide a complete characterization of optimal distortion for low and high sampling rates (with respect to the signal bandwidth). We also provide bounds on the reconstruction distortion for rates in the intermediate region. It is shown that nonuniform sampling outperforms uniform sampling for low sampling rates. In addition, the optimal nonuniform sampling set is robust with respect to missing sampling values. On the other hand, for the sampling rates above the Nyquist rate, the uniform sampling strategy is optimal. © 1963-2012 IEEE
  6. Keywords:
  7. Distortion ; Sampling locations ; Bandwidth ; Commerce ; Communication channels (information theory) ; Distortion (waves) ; Gaussian noise (electronic) ; Mathematical models ; Random variables ; Sampling ; White noise ; Additive white Gaussian noise ; Arbitrary sampling rates ; High sampling rates ; Noise measurements ; Nonuniform sampling ; Phase distortions ; Reconstruction distortion ; Sampling location ; Signal sampling
  8. Source: IEEE Transactions on Information Theory ; Volume 64, Issue 3 , March , 2018 , Pages 1706-1724 ; 00189448 (ISSN)
  9. URL: https://ieeexplore.ieee.org/document/8187684