A Family of Wavelets and a new Orthogonal Multiresolution Analysis Based on the Nyquist Criterion

TL;DR

This paper introduces a new family of orthogonal complex wavelets based on the Nyquist criterion, derived from a generalization of Shannon wavelets and related to raised cosine filters, with applications in ISI elimination.

Contribution

It presents a novel family of wavelets and an orthogonal multiresolution analysis based on Nyquist criterion, including a generalization of raised cosine wavelets.

Findings

Roll-off parameter should be below 1/3 for optimal MRA

Asymmetry observed in pass-band Fourier spectrum regions

Generalized raised cosine wavelets proposed

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.