A Family of Wavelets and a new Orthogonal Multiresolution Analysis Based on the Nyquist Criterion
Classical Analysis and ODEs
2016-03-24 v2
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.
Keywords
Cite
@article{arxiv.1503.00766,
title = {A Family of Wavelets and a new Orthogonal Multiresolution Analysis Based on the Nyquist Criterion},
author = {H. M. de Oliveira and L. R. Soares and T. H. Falk},
journal= {arXiv preprint arXiv:1503.00766},
year = {2016}
}
Comments
8 pages, 14 figures