On the construction of band-limited wavelets with the Prouhet–Thue–Morse sequence

This paper investigates the use of invariant cycles to construct band-limited wavelets. We generalize the construction of Lemarié–Meyer wavelets by relaxing the condition on the supports of the low-pass filters. We show that the Prouhet–Thue–Morse constant has an important connection with the measure of the support of the infinite product of the low-pass filter, and the band-limited wavelets with low-pass filters have larger supports than do the Lemarié–Meyer wavelets.