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Finding the Minimum Sampling Frequency of Multi-band Signals: An Efficient Iterative Algorithm

This paper presents an efficient iterative algorithm designed to determine the minimum sampling frequency for multi-band signals, addressing the issue of alias-free sampling. The authors formulate the problem and build upon previous works to introduce a new set of conditions that ensure alias-free sampling. Through detailed simulations and comparisons, the proposed algorithm is validated, demonstrating its effectiveness and efficiency in real-world applications. Key lemmas are provided to support the theoretical foundations of the approach, ensuring it meets the alias-free conditions.

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Finding the Minimum Sampling Frequency of Multi-band Signals: An Efficient Iterative Algorithm

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  1. Finding the Minimum Sampling Frequency of Multi-band Signals: An Efficient Iterative Algorithm Yuan-Pei Lin, Yi-De Liu, See-May Phoong

  2. Outline • Problem Formulation • Previous Works • A New Set of Conditions for Alias-Free Sampling • The Proposed Iterative Algorithm • Simulations and Comparisons • Conclusion

  3. Problem Formulation

  4. Previous Works:One-bandpass (2 bands) Case

  5. Previous Works

  6. The Proposed Algorithm

  7. A New Set of Alias-Free Sampling Conditions

  8. Lemma 1

  9. Lemma 1 – proof (1)

  10. Lemma 1 – proof (2)

  11. Lemma 1 – proof (3)

  12. Alias-Free Conditions

  13. Lemma 2

  14. Lemma 2 – proof (1)

  15. Lemma 2 – proof (2)

  16. Meeting the Alias-Free Sampling Conditions

  17. Proposed Iterative Algorithm

  18. Simulation and Comparison

  19. Simulation and Comparison

  20. Conclusions

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