Polynomial Wavelets on [-1, 1

Abstract

A new approach to polynomial wavelets on the interval [-1, 1] is presented. Our method is based on the Chebyshev transform, corresponding shifts and discrete cosine transform (DCT). The considered scaling function of level j (j ∈ ℕ0) is a polynomial which fulfils special interpolation conditions with respect to the nodes cos (kπ/2 j ) (k = 0, ..., 2 j ). Using fast DCT-algorithms, efficient decomposition and reconstruction algorithms are proposed.