Wavelet transforms associated with finite cyclic groups

Giuseppe Caire, Robert L. Grossman, H. Vincent Poor

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

Generally speaking, the principal framework within which multiresolution techniques have been studied and applied is the same as that used in the discretetime Fourier analysis of sequences of complex numbers. This paper develops an analogous framework for the multiresolution analysis of finite-length sequences of elements from arbitrary fields. As in finite-length Fourier analysis, a cyclic group structure of the index set of such sequences is exploited to characterize the transforms of interest for the particular cases of complex and finite fields. This development is motivated by potential applications in areas such as digital signal processing and algebraic coding, in which cyclic Fourier analysis has found widespread applications.

Original languageEnglish (US)
Title of host publicationConference Record of the 26th Asilomar Conference on Signals, Systems and Computers, ACSSC 1992
PublisherIEEE Computer Society
Pages113-119
Number of pages7
ISBN (Electronic)0818631600
DOIs
StatePublished - Jan 1 1992
Event26th Asilomar Conference on Signals, Systems and Computers, ACSSC 1992 - Pacific Grove, United States
Duration: Oct 26 1992Oct 28 1992

Publication series

NameConference Record - Asilomar Conference on Signals, Systems and Computers
ISSN (Print)1058-6393

Conference

Conference26th Asilomar Conference on Signals, Systems and Computers, ACSSC 1992
CountryUnited States
CityPacific Grove
Period10/26/9210/28/92

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Computer Networks and Communications

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    Caire, G., Grossman, R. L., & Poor, H. V. (1992). Wavelet transforms associated with finite cyclic groups. In Conference Record of the 26th Asilomar Conference on Signals, Systems and Computers, ACSSC 1992 (pp. 113-119). [269247] (Conference Record - Asilomar Conference on Signals, Systems and Computers). IEEE Computer Society. https://doi.org/10.1109/ACSSC.1992.269247