Designing local orthogonal bases on finite groups I: Abelian case

Riccardo Bernardini, Jelena Kovačević

Research output: Contribution to journalArticlepeer-review


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 considers abelian groups. The second part considers nonabelian groups where, as an example, we show how to build such bases where the group of unitary transformations consists of modulations and rotations. These bases are useful for building systems for evaluating image quality.

Original languageEnglish (US)
Pages (from-to)1-23
Number of pages23
JournalJournal of Fourier Analysis and Applications
Issue number1
StatePublished - 2000

ASJC Scopus subject areas

  • Analysis
  • General Mathematics
  • Applied Mathematics


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