A Family of Wavelets and a New Orthogonal Multiresolution Analysis Based on the Nyquist Criterion<br />10.14209/jcis.2003.8

  • Hélio Magalhães de Oliveira
  • Luciana Reginaldo Soares
  • Tiago Henrique Falk

Abstract

A generalisation of the Shannon complex wavelet is introduced, which is related to raised cosine filters. This approach is then used to derive a new family of orthogonal complex wavelets based on the Nyquist criterion for Inter-symbolic Interference (lSI) 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. A generalisation of the (square root) raised cosine wavelets is proposed. Finally, a computational implementation of such wavelets on Matlab™ is presented as well as a few applications.
Published
18-06-2015
How to Cite
Magalhães de Oliveira, H., Reginaldo Soares, L., & Henrique Falk, T. (2015). A Family of Wavelets and a New Orthogonal Multiresolution Analysis Based on the Nyquist Criterion<br /&gt;10.14209/jcis.2003.8. Journal of Communication and Information Systems, 18(1). Retrieved from https://jcis.sbrt.org.br/jcis/article/view/327
Section
Regular Papers