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

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.

preprint2015arXivOpen access
H. M. de OliveiraL. R. SoaresT. H. Falk
math.CA
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H. M. de OliveiraL. R. SoaresT. H. Falk

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