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

DOI: 10.14209/its.2002.383

Evento: 2002 International Telecommunications Symposium (ITS2002)

Keywords: Multiresolution Analysis Wavelets Nyquist Criterion Intersymbolic Interference (ISI).

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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