Fourier Analysis of Sequences over a Composition Algebra of the Real Number Field

• MAEDA Takao

  School of Computer Science and Engineering, University of Aizu

• HAYASHI Takafumi

  School of Computer Science and Engineering, University of Aizu

Abstract

To analyze the structure of a set of perfect sequences over a composition algebra of the real number field, transforms of a set of sequences similar to the discrete Fourier transform (DFT) are introduced. The discrete cosine transform, discrete sine transform, and generalized discrete Fourier transform (GDFT) of the sequences are defined and the fundamental properties of these transforms are proved. We show that GDFT is bijective and that there exists a relationship between these transforms and a convolution of sequences. Applying these properties to the set of perfect sequences, a parameterization theorem of such sequences is obtained.

Journal

• IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

  IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E96.A (12), 2452-2456, 2013

  The Institute of Electronics, Information and Communication Engineers

Keywords

• Fourier analysis
• convolution
• composition algebra
• correlation function
• perfect sequence

Details

• CRID: 1390001206312215680
• NII Article ID: 130003385296
• NII Book ID: AA10826239
• DOI: 10.1587/transfun.e96.a.2452
• ISSN: 17451337
• ISSN: 09168508
• NDL BIB ID: 025051005
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I025051005
• Web Site: https://www.jstage.jst.go.jp/article/transfun/E96.A/12/E96.A_2452/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed