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Walsh Functions with Barycentric Symmetry over Triangular Domain

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DOI: 10.23977/tracam.2024.040105 | Downloads: 4 | Views: 236

Author(s)

Bowen Jiang 1

Affiliation(s)

1 School of Artificial Intelligence and Computer Science, Jiangnan University, Wuxi, Jiangsu Province, 214122, China

Corresponding Author

Bowen Jiang

ABSTRACT

The Walsh function is a complete set of orthogonal functions defined on the interval [0, 1], with values fixed at either +1 or -1. The function demonstrates the beauty of symmetry in mathematics and plays a unique role in applications. This paper focuses on the Walsh function over the trigonometric domain and develops a set of completely orthogonal functions over the trigonometric domain. The results illustrate the symmetry of these functions in both mathematical form and the barycentric coordinate system.

KEYWORDS

Walsh function, orthogonality, triangular domain, barycentric symmetry

CITE THIS PAPER

Bowen Jiang, Walsh Functions with Barycentric Symmetry over Triangular Domain. Transactions on Computational and Applied Mathematics (2024) Vol. 4: 36-40. DOI: http://dx.doi.org/10.23977/tracam.2024.040105.

REFERENCES

[1] Guan Z, Chen W. Walsh functions and Walsh transformations [M]. National Defense Industry Press. 1984.
[2] Liu Z. Orthogonal functions and their applications [M]. National Defense Industry Press. 1982:162-181.
[3] Feng Y, Qi D. On The Haar and Walsh Syst4ems on a triangle [J]. Journal of Computational Mathematics. 1983: 223-232.
[4] Qi D. A new definition of self-similar structure and Walsh function [J]. Chinese Annals of Mathematics. 1991; A6: 103-105.

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