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Generalized Cardinal Polishing Splines Signal Reconstruction

Author

Listed:
  • Fangli Sun

    (School of Computer Science and Engineering, Macau University of Science and Technology, Taipa, Macau 999078, China)

  • Zhanchuan Cai

    (School of Computer Science and Engineering, Macau University of Science and Technology, Taipa, Macau 999078, China
    Zhuhai MUST Science and Technology Research Institute, Zhuhai 519099, China)

Abstract

Sampling and reconstruction are indispensable processes in signal processing, and appropriate foundations are crucial for spline reconstruction models. Generalized cardinal polishing splines (GCP-splines) are a class of high-precision explicit splines with pretty properties. We propose the theory of GCP-splines for signal reconstruction and differential signaling to improve signal reconstruction accuracy. First, the elementary theory of the GCP-splines signal processing is proposed, and it mainly includes Fourier transformation and Z-transformation of the GCP-splines. Then, a GCP-splines filter that can be used to reconstruct the output signal from the input discrete signal is proposed. Next, we propose differential signal reconstruction based on the GCP-splines and the sampled original signal values to obtain information on the signal change rate. Numerical experiments demonstrate that the signal reconstruction based on the GCP-splines yields lower approximation errors and better performance than the linear interpolation filter and cardinal B-spline interpolation filter.

Suggested Citation

  • Fangli Sun & Zhanchuan Cai, 2025. "Generalized Cardinal Polishing Splines Signal Reconstruction," Mathematics, MDPI, vol. 13(6), pages 1-18, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:6:p:983-:d:1614124
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    References listed on IDEAS

    as
    1. Vangelis Marinakis & Athanassios S. Fokas & George A. Kastis & Nicholas E. Protonotarios, 2023. "Chebyshev Interpolation Using Almost Equally Spaced Points and Applications in Emission Tomography," Mathematics, MDPI, vol. 11(23), pages 1-14, November.
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