Boosted Whittaker-Henderson Graduation of Order 1: A Graph Spectral Filter Using Discrete Cosine Transform

Authors

  • Ruoyi Bao Graduate School of Humanities and Social Sciences, Hiroshima University, 1-2-1 Kagamiyama, Higashihiroshima 739-8525, Japan https://orcid.org/0009-0008-2826-6157
  • Hiroshi Yamada Graduate School of Humanities and Social Sciences, Hiroshima University, 1-2-1 Kagamiyama, Higashihiroshima 739-8525, Japan https://orcid.org/0000-0001-5560-0319

DOI:

https://doi.org/10.37256/cm.6220254409

Keywords:

Whittaker-Henderson graduation, boosted Hodrick-Prescott filter, graph Laplacian, graph spectral filter, discrete cosine transform

Abstract

The Whittaker-Henderson (WH) graduation of order 1 is a smoothing/filtering method for equally spaced one-dimensional data. Inspired by Phillips and Shi, this paper introduces the boosted version of the WH graduation of order 1. We show that it is a graph spectral filter using the discrete cosine transform, and then provide a simple formula for the (i, j) entry of its smoother matrix. We also show that it is a linear smoother such that the filter weights sum to unity and the smoother matrix is bisymmetric, i.e., symmetric and centrosymmetric. GNU Octave user-defined functions based on the obtained results are also provided.

References

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Published

2025-03-20

Issue

Contemporary Mathematics, Volume 6 Issue 2 (2025), 1380-2725

Section

Research Article

License

Copyright (c) 2025 Ruoyi Bao, et al.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

1.
Boosted Whittaker-Henderson Graduation of Order 1: A Graph Spectral Filter Using Discrete Cosine Transform. Contemp. Math. [Internet]. 2025 Mar. 20 [cited 2025 Dec. 24];6(2):2027-3. Available from: https://ojs353.mebyme.cn/index.php/CM/article/view/4409