39. 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 elimination. An orthogonal Multiresolution Analysis 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.