Cyclic wavelet transforms for arbitrary finite data lengths

Sandip Sarkar, H. Vincent Poor

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

Multiresolution analysis via decomposition into wavelets has been established as an important transform technique in signal processing. A wealth of results is available on this subject, and particularly, the framework has been extended to treat finite length sequences of size 2n (for positive integers n) over finite fields. The present paper extends this idea further to provide a framework for dealing with arbitrary finite data lengths. This generalization is largely motivated in part by the need for such transforms for building error correcting codes in the wavelet transform domain. Here we extend the previous two-band formulation of the transform to treat a p-band case in general (i.e. for data length pn), where p is a prime number, and we also give a general result for developing transforms over composite-length sequences. Potential applications and computational complexity issues are discussed as well.

Original languageEnglish (US)
Pages (from-to)2541-2552
Number of pages12
JournalSignal Processing
Volume80
Issue number12
DOIs
StatePublished - Dec 2000

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Electrical and Electronic Engineering

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