EXACT RECONSTRUCTION ALGORITHMS FOR THE DISCRETE WAVELET TRANSFORM USING SPLINE-WAVELETS

By making a discrete finite time signal periodic, it is shown that non orthogonal B-spline wavelets can be used in a discrete wavelet transfo rm with exact decomposition and reconstruction. A nonrecursive algorit hm using only Finite Impulse Response filters (FIR) with complexity O( N-2) is presented. The complexity is reduced to O(N log(2) N) by using Fast Fourier Transforms (FFT). A faster algorithm is obtained by usin g recursive filters in the decomposition or reconstruction of the sign al. The recursive algorithm has complexity O(N), and the same accuracy as the others. By allowing nonsymmetric wavelets, an exact orthogonal reconstruction algorithm is shown, which also has complexity O(N). (C ) 1995 Academic Press, Inc