49. Chebyshev Wavelets

In this note we introduce a new family of wavelets, named Chebyshev wavelets,
which are derived from conventional Chebyshev polynomials.
Properties of Chebyshev filter banks are investigated, including orthogonality and
perfect reconstruction conditions. Chebyshev wavelets of 2nd kind have compact support,

their filters possess good
selectivity, but they are not orthogonal.
The convergence into 2nd kind Chebyshev wavelets via the cascade algorithm is proved
by using Markov chains theorems. Computational implementation of these wavelets
and some clear-cut applications are presented. These wavelets are offered as a choice in wavelet analysis.