  In this paper we introduce a new family of wavelets, named Chebyshev
wavelets, which are derived from conventional first and second kind Chebyshev
polynomials. Properties of Chebyshev filter banks are investigated, including
orthogonality and perfect reconstruction conditions. Chebyshev wavelets have
compact support, their filters possess good selectivity, but they are not
orthogonal. The convergence of the cascade algorithm of Chebyshev wavelets is
proved by using properties of Markov chains. Computational implementation of
these wavelets and some clear-cut applications are presented. Proposed wavelets
are suitable for signal denoising.
