On the construction of wavelets on a bounded interval

Gerlind Plonka (1) , Kathi Selig (1) , Manfred Tasche (1)

1 Institut für Mathematik [Rostock]

This paper presents a general approach to a multi resolution analysis and wavelet spaces on the interval $[-1, 1]$. Our method is based on the Chebyshev transform, corresponding shifts and the discrete cosine transformation (DCT). For the wavelet analysis of given functions, efficient decomposition and reconstruction algorithms are proposed using fast DCT-algorithms. As examples for scaling functions and wavelets, polynomials and transformed splines are considered.

Mots clés: Wavelet; Chebyshev transform

Domaines: Mathématiques [math]

Gerlind Plonka, Kathi Selig, Manfred Tasche. On the construction of wavelets on a bounded interval. Advances in Computational Mathematics, 1995, 4, pp.357-388. ⟨10.1007/BF02123481⟩. ⟨hal-01322918⟩