A Family of Wavelets and a New Orthogonal Multiresolution Analysis Based on the Nyquist Criterion10.14209/jcis.2003.8 - Magalhães de Oliveira, Hélio; Reginaldo Soares, Luciana; Henrique Falk, Tiago (Journal of Communication and Information Systems, 2015)
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.