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Generalized Orthogonal Discrete W Transform and Its Fast Algorithm

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  • Jichao Sun
  • Zhengping Zhang
  • Stefania Tomasiello

Abstract

Based on the generalized discrete Fourier transform, the generalized orthogonal discrete W transform and its fast algorithm are proposed and derived in this paper. The orthogonal discrete W transform proposed by Zhongde Wang has only four types. However, the generalized orthogonal discrete W transform proposed by us has infinite types and subsumes a family of symmetric transforms. The generalized orthogonal discrete W transform is a real-valued orthogonal transform, and the real-valued orthogonal transform of a real sequence has the advantages of simple operation and facilitated transmission and storage. The generalized orthogonal discrete W transforms provide more basis functions with new frequencies and phases and hence lead to more powerful analysis and processing tools for communication, signal processing, and numerical computing.

Suggested Citation

  • Jichao Sun & Zhengping Zhang & Stefania Tomasiello, 2021. "Generalized Orthogonal Discrete W Transform and Its Fast Algorithm," Discrete Dynamics in Nature and Society, Hindawi, vol. 2021, pages 1-13, January.
    • Handle: RePEc:hin:jnddns:2529754
    DOI: 10.1155/2021/2529754
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