Fast Multiparameter Walsh, Chrestenson – Vilenkin and Haar Transforms

Authors

  • V. G. Labunets Ural Federal University named after the first President of Russia B.N.Yeltsin
  • S. A. Martyugin Ural Federal University named after the first President of Russia B.N.Yeltsin; SPA Automatics, named after Academician N.A. Semikhatov

DOI:

https://doi.org/10.14529/ctcr160416

Keywords:

Fourier Transform, Walsh Transform, Chrestenson-Vilenkin Transform, Haar Transform, Fractional and multiparameter transforms, signal and image processing

Abstract

In this article the new class of multiparameter and fractional Walsh Krestensona-Vilenkin and Haar transforms for the adaptive spectrum analysis of signals is provided and quick algorithms are developed for these conversions. Fractional one-parameter conversions are the special case of these multiparameter conversions. The systematic method of synthesis of multiparameter symmetric and asymmetrical conversions is provided. In case of the smooth change of parameters multiparameter conversions change the form from identical conversions to classical smoothly that allows to enter adaptation elements into spectrum analysis of signals. Basis functions of Walsh transforms and Haar can be used as subcarriers in the generalized OFDM and CDMA systems.

Author Biographies

V. G. Labunets, Ural Federal University named after the first President of Russia B.N.Yeltsin

д-р техн. наук, профессор, кафедра теоретических основ радиотехники

S. A. Martyugin, Ural Federal University named after the first President of Russia B.N.Yeltsin; SPA Automatics, named after Academician N.A. Semikhatov

аспирант; инженер

References

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Published

2016-12-05

Issue

Vol. 16 No. 4 (2016)

Section

Short messages