Two-Dimensional Clifford Windowed Fourier Transform

  • Mawardi BahriEmail author
  • Eckhard M. S. Hitzer
  • Sriwulan Adji


Recently several generalizations to higher dimension of the classical Fourier transform (FT) using Clifford geometric algebra have been introduced, including the two-dimensional (2D) Clifford–Fourier transform (CFT). Based on the 2D CFT, we establish the two-dimensional Clifford windowed Fourier transform (CWFT). Using the spectral representation of the CFT, we derive several important properties such as shift, modulation, a reproducing kernel, isometry, and an orthogonality relation. Finally, we discuss examples of the CWFT and compare the CFT and CWFT.


Fringe Pattern Window Function Clifford Algebra Geometric Algebra Scalar Part 
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Copyright information

© Springer-Verlag London 2010

Authors and Affiliations

  • Mawardi Bahri
    • 1
    Email author
  • Eckhard M. S. Hitzer
    • 2
  • Sriwulan Adji
    • 1
  1. 1.School of Mathematical SciencesUniversiti Sains MalaysiaPenangMalaysia
  2. 2.Department of Applied PhysicsUniversity of FukuiFukuiJapan

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