Skip to main content
SpringerLink
Log in

Designing local orthogonal bases on finite groups II: Nonabelian case

  • Published:
Journal of Fourier Analysis and Applications Aims and scope Submit manuscript

Abstract

We extend to general finite groups a well-known relation used for checking the orthogonality of a system of vectors as well as for orthogonalizing a nonorthogonal one. This in turn, is used for designing local orthogonal bases obtained by unitary transformations of a single prototype filter. The first part of this work considered the abelian groups of unitary transformations, while here we deal with nonabelian groups. As an example, we show how to build such bases where the group of unitary transformations consists of modulation and rotations. Such bases are useful for building systems for evaluation image quality.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bernardini, R. and Kovačević, J. (2000). Designing local orthogonal bases on finite groups I: Abelian case,J. Fourier Anal. Appl. 6(1).

  2. Vetteri, M. and Kovačević, J. (1995).Signal Processing, inWavelets and Subband Coding, Prentice-Hall, Englewood Cliffs, NJ

    Google Scholar 

  3. Bernardini, R. and Kovačević, J. (1996–1997). Local orthogonal bases I: Construction,Multidim. Syst. and Signal Proc., special issue on Wavelets and Multiresolution Signal Processing,7, 331–370, July. Invited paper. Reprinted inMultidimensional Filter Banks and Wavelets, Basu, S. and Levy, B., Eds., Kluwer Academic Publishers.

    MATH  Google Scholar 

  4. Bernardini, R. and Kovačević, J. (1996–1997). Local orthogonal bases II: Window design,Multidim. Syst and Signal Proc., special issue on Wavelets and Multiresolution Signal Processing,7, 371–400, July. Invited paper. Reprinted inMultidimensional Filter Banks and Wavelets, Basu, S. and Levy. B., Eds., Kluwer Academic Publishers.

    MATH  Google Scholar 

  5. Malvar, H. (1992).Signal Processing with Lapped Transforms, Artech House, Norwood, MA.

    MATH  Google Scholar 

  6. Serr, J. (1971).Linear Representations of Finite Groups. Springer-Verlag, New York.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Padova, 35131, Padova, Italy

    Riccardo Bernardini

  2. Bell Laboratories, 07974, Murray Hill, NJ, USA

    Jelena Kovačević

Authors
  1. Riccardo Bernardini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jelena Kovačević
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bernardini, R., Kovačević, J. Designing local orthogonal bases on finite groups II: Nonabelian case. The Journal of Fourier Analysis and Applications 6, 207–231 (2000). https://doi.org/10.1007/BF02510661

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02510661

Keywords

Search

Navigation