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A Family of Wavelets and a new Orthogonal Multiresolution Analysis Based on the Nyquist Criterion

Authors
  • de Oliveira, H. M.
  • Soares, L. R.
  • Falk, T. H.
Type
Published Article
Publication Date
Mar 05, 2015
Submission Date
Feb 12, 2015
Identifiers
DOI: 10.14209/jcis.2003.8
Source
arXiv
License
Yellow
External links

Abstract

A generalisation of the Shannon complex wavelet is introduced, which is related to raised cosine filters. This approach is used to derive a new family of orthogonal complex wavelets based on the Nyquist criterion for Intersymbolic Interference (ISI) elimination. An orthogonal Multiresolution Analysis (MRA) is presented, showing that the roll-off parameter should be kept below 1/3. The pass-band behaviour of the Wavelet Fourier spectrum is examined. The left and right roll-off regions are asymmetric; nevertheless the Q-constant analysis philosophy is maintained. Finally, a generalisation of the (square root) raised cosine wavelets is proposed.

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