A Family of Wavelets and a New Orthogonal Multiresolution Analysis Based on the Nyquist Criterion
H. M. de Oliveira, L. R. Soares, T. H. Falk · Anais do 2002 International Telecommunications Symposium · 2002
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.