46. On Filter Banks and Wavelets Based on Chebyshev Polynomials


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 of the cascade algorithm of
2nd kind Chebyshev wavelets is proved by using properties of Markov chains.
Computational implementation of these wavelets and some clear-cut applications are presented.
These wavelets are offered as a choice in wavelet analysis.