ON THE COMPUTATION OF PERIODIC SPLINE-WAVELETS

For many applications in signal processing and numerical analysis, it is important to use periodic scaling functions and wavelets. The aim o f this paper is a constructive approach to periodic spline wavelets an d to related decomposition and reconstruction algorithms. We apply the periodization of the semiorthogonal Chui-Wang wavelets and the well-k nown Euler-Frobenius functions. Using a new approach to the decomposit ion relations via two-scale symbol (2,2)-matrices, we obtain new and e fficient decomposition and reconstruction algorithms which are mainly based on the fast Fourier transform technique. The presented algorithm s can be used for the decomposition and reconstruction of L(2)(R)-func tions, too. Finally, our decomposition algorithm is used to analyze th e local regularity of periodic functions. (C) 1995 Academic Press, Inc .